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Proof step 81 from proof inv-rename-new-reparent (previous step)

fs0[ri0[dentrykey(m, str)]] = dentrynode(key1, m3), fs0[ri0[inodekey(m3)]] = inodenode(key0, md1, boolvar0, m5, m9, m10), fs0[ri0[inodekey(m0)]] = inodenode(key2, md3, true, m6, m7, m8), fo.inodes?, ro.inodes?, file-node-cons(fs0, ri0), log-cons(log0, fs0), orphans-cons(fs0, ri0, ro), replay-cons-strong(fs0, ri0, ro, fi, fo, log0), ri-inj(fi), ri-inj(ri0), ubifs-cons(fs0, ri0, ro, fi, fo, log0), dentrykey(m, str) ∈ ri0, inodekey(m3) ∈ ri0, inodekey(m0) ∈ ri0, ri0[dentrykey(m, str)] ∈ fs0, ri0[inodekey(m3)] ∈ fs0, inodekey(m) ∈ ri0, ri0[inodekey(m0)] ∈ fs0, ri0[inodekey(m)] ∈ fs0, key ∈ ri0 → ri0[key] ∈ fs0 ∧ fs0[ri0[key]].key = key ∧ (key.inode? → fs0[ri0[key]].inode?) ∧ ( key.dentry? → fs0[ri0[key]].dentry? ∧ inodekey(key.ino) ∈ ri0 ∧ inodekey(fs0[ri0[key]].ino) ∈ ri0 ∧ ¬ inodekey(key.ino) ∈ ro ∧ ¬ inodekey(fs0[ri0[key]].ino) ∈ ro ∧ fs0[ri0[inodekey(key.ino)]].directory) ∧ (key.data? → fs0[ri0[key]].data? ∧ inodekey(key.ino) ∈ ri0 ∧ ¬ fs0[ri0[inodekey(key.ino)]].directory ∧ # fs0[ri0[key]].data = VFS_PAGE_SIZE), m2 ≠ 0 ∨ m = ROOT_INO, m6 ≠ 0 ∨ m0 = ROOT_INO, ¬ boolvar0 ∧ ¬ boolvar2 ∨ boolvar0 ∧ boolvar2 ∧ m4 = m10, key = inodekey(m) ∨ key = dentrykey(m0, str0) ∨ key ≠ dentrykey(m, str) ∧ key ∈ ri0 ⊦ key.ino = 0, adr1 = adr4, adr1 = adr3, adr1 = adr2, adr2 = adr4, adr2 = adr3, adr3 = adr4, key = inodekey(m0), m = 0, m0 = m, m0 = 0, adr3 ∈ (ri0 -- dentrykey(m, str))[dentrykey(m0, str0), adr2], inodekey(m) ∈ ro, dentrykey(m0, str0) ∈ ri0, inodekey(m0) ∈ ro, adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0, adr4 ∈ fs0, adr2 ∈ ri0 -- dentrykey(m, str), adr4 ∈ (ri0 -- dentrykey(m, str))[dentrykey(m0, str0), adr2][inodekey(m), adr3], ( (inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) = adr4 ∨ (inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) = adr3 ∨ (inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) = adr2 ∨ (inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) = adr1 ∨ (inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ∈ fs0) ∧ (adr4 = (inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ⊃ inodenode(inodekey(m0), md0, true, m6, m7 + (boolvar2 ⊃ 1;0), m8 + 1) ;(adr3 = (inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ⊃ inodenode(inodekey(m), md, true, m2, n0, m1) ;(adr2 = (inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ⊃ dentrynode(dentrykey(m0, str0), m3) ;(adr1 = (inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ⊃ dentrynode(dentrykey(m, str), 0) ;fs0[(inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key])))] ) ) ) ) .key = key ∧ ( key.inode? → (adr4 = (inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ⊃ inodenode(inodekey(m0), md0, true, m6, m7 + (boolvar2 ⊃ 1;0), m8 + 1) ;(adr3 = (inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ⊃ inodenode(inodekey(m), md, true, m2, n0, m1) ;(adr2 = (inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ⊃ dentrynode(dentrykey(m0, str0), m3) ;(adr1 = (inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ⊃ dentrynode(dentrykey(m, str), 0) ;fs0[(inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key])))] ) ) ) ) .inode?) ∧ ( key.dentry? → (adr4 = (inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ⊃ inodenode(inodekey(m0), md0, true, m6, m7 + (boolvar2 ⊃ 1;0), m8 + 1) ;(adr3 = (inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ⊃ inodenode(inodekey(m), md, true, m2, n0, m1) ;(adr2 = (inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ⊃ dentrynode(dentrykey(m0, str0), m3) ;(adr1 = (inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ⊃ dentrynode(dentrykey(m, str), 0) ;fs0[(inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key])))] ) ) ) ) .dentry? ∧ inodekey(key.ino) ∈ ri0 ∧ ( (adr4 = (inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ⊃ inodenode(inodekey(m0), md0, true, m6, m7 + (boolvar2 ⊃ 1;0), m8 + 1) ;(adr3 = (inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ⊃ inodenode(inodekey(m), md, true, m2, n0, m1) ;(adr2 = (inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ⊃ dentrynode(dentrykey(m0, str0), m3) ;(adr1 = (inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ⊃ dentrynode(dentrykey(m, str), 0) ;fs0[(inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key])))] ) ) ) ) .ino = m0 ∨ (adr4 = (inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ⊃ inodenode(inodekey(m0), md0, true, m6, m7 + (boolvar2 ⊃ 1;0), m8 + 1) ;(adr3 = (inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ⊃ inodenode(inodekey(m), md, true, m2, n0, m1) ;(adr2 = (inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ⊃ dentrynode(dentrykey(m0, str0), m3) ;(adr1 = (inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ⊃ dentrynode(dentrykey(m, str), 0) ;fs0[(inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key])))] ) ) ) ) .ino = m ∨ inodekey ((adr4 = (inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ⊃ inodenode(inodekey(m0), md0, true, m6, m7 + (boolvar2 ⊃ 1;0), m8 + 1) ;(adr3 = (inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ⊃ inodenode(inodekey(m), md, true, m2, n0, m1) ;(adr2 = (inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ⊃ dentrynode(dentrykey(m0, str0), m3) ;(adr1 = (inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ⊃ dentrynode(dentrykey(m, str), 0) ;fs0[(inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key])))] ) ) ) ) .ino) ∈ ri0) ∧ ¬ inodekey(key.ino) ∈ ro ∧ ¬ inodekey ((adr4 = (inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ⊃ inodenode(inodekey(m0), md0, true, m6, m7 + (boolvar2 ⊃ 1;0), m8 + 1) ;(adr3 = (inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ⊃ inodenode(inodekey(m), md, true, m2, n0, m1) ;(adr2 = (inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ⊃ dentrynode(dentrykey(m0, str0), m3) ;(adr1 = (inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ⊃ dentrynode(dentrykey(m, str), 0) ;fs0[(inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key])))] ) ) ) ) .ino) ∈ ro ∧ (adr4 = (m0 = key.ino ⊃ adr4;(m = key.ino ⊃ adr3;ri0[inodekey(key.ino)])) ⊃ inodenode(inodekey(m0), md0, true, m6, m7 + (boolvar2 ⊃ 1;0), m8 + 1) ;(adr3 = (m0 = key.ino ⊃ adr4;(m = key.ino ⊃ adr3;ri0[inodekey(key.ino)])) ⊃ inodenode(inodekey(m), md, true, m2, n0, m1) ;(adr2 = (m0 = key.ino ⊃ adr4;(m = key.ino ⊃ adr3;ri0[inodekey(key.ino)])) ⊃ dentrynode(dentrykey(m0, str0), m3) ;(adr1 = (m0 = key.ino ⊃ adr4;(m = key.ino ⊃ adr3;ri0[inodekey(key.ino)])) ⊃ dentrynode(dentrykey(m, str), 0) ;fs0[(m0 = key.ino ⊃ adr4;(m = key.ino ⊃ adr3;ri0[inodekey(key.ino)]))] ) ) ) ) .directory) ∧ ( key.data? → (adr4 = (inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ⊃ inodenode(inodekey(m0), md0, true, m6, m7 + (boolvar2 ⊃ 1;0), m8 + 1) ;(adr3 = (inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ⊃ inodenode(inodekey(m), md, true, m2, n0, m1) ;(adr2 = (inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ⊃ dentrynode(dentrykey(m0, str0), m3) ;(adr1 = (inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ⊃ dentrynode(dentrykey(m, str), 0) ;fs0[(inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key])))] ) ) ) ) .data? ∧ inodekey(key.ino) ∈ ri0 ∧ ¬ (adr4 = (m0 = key.ino ⊃ adr4;(m = key.ino ⊃ adr3;ri0[inodekey(key.ino)])) ⊃ inodenode(inodekey(m0), md0, true, m6, m7 + (boolvar2 ⊃ 1;0), m8 + 1) ;(adr3 = (m0 = key.ino ⊃ adr4;(m = key.ino ⊃ adr3;ri0[inodekey(key.ino)])) ⊃ inodenode(inodekey(m), md, true, m2, n0, m1) ;(adr2 = (m0 = key.ino ⊃ adr4;(m = key.ino ⊃ adr3;ri0[inodekey(key.ino)])) ⊃ dentrynode(dentrykey(m0, str0), m3) ;(adr1 = (m0 = key.ino ⊃ adr4;(m = key.ino ⊃ adr3;ri0[inodekey(key.ino)])) ⊃ dentrynode(dentrykey(m, str), 0) ;fs0[(m0 = key.ino ⊃ adr4;(m = key.ino ⊃ adr3;ri0[inodekey(key.ino)]))] ) ) ) ) .directory ∧ # (adr4 = (inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ⊃ inodenode(inodekey(m0), md0, true, m6, m7 + (boolvar2 ⊃ 1;0), m8 + 1) ;(adr3 = (inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ⊃ inodenode(inodekey(m), md, true, m2, n0, m1) ;(adr2 = (inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ⊃ dentrynode(dentrykey(m0, str0), m3) ;(adr1 = (inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ⊃ dentrynode(dentrykey(m, str), 0) ;fs0[(inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key])))] ) ) ) ) .data = VFS_PAGE_SIZE)

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 82:
fs0[ri0[inodekey(m0)]] = inodenode(key2, md3, true, m6, m7, m8), fs0[ri0[inodekey(m3)]] = inodenode(key0, md1, boolvar0, m5, m9, m10), fs0[ri0[dentrykey(m, str)]] = dentrynode(key1, m3), ro.inodes?, fo.inodes?, file-node-cons(fs0, ri0), log-cons(log0, fs0), orphans-cons(fs0, ri0, ro), replay-cons-strong(fs0, ri0, ro, fi, fo, log0), ri-inj(ri0), ri-inj(fi), ubifs-cons(fs0, ri0, ro, fi, fo, log0), ri0[inodekey(m)] ∈ fs0, ri0[inodekey(m0)] ∈ fs0, inodekey(m) ∈ ri0, ri0[inodekey(m3)] ∈ fs0, ri0[dentrykey(m, str)] ∈ fs0, inodekey(m0) ∈ ri0, inodekey(m3) ∈ ri0, dentrykey(m, str) ∈ ri0, key ∈ ri0 → ri0[key] ∈ fs0 ∧ fs0[ri0[key]].key = key ∧ (key.inode? → fs0[ri0[key]].inode?) ∧ ( key.dentry? → fs0[ri0[key]].dentry? ∧ inodekey(key.ino) ∈ ri0 ∧ inodekey(fs0[ri0[key]].ino) ∈ ri0 ∧ ¬ inodekey(key.ino) ∈ ro ∧ ¬ inodekey(fs0[ri0[key]].ino) ∈ ro ∧ fs0[ri0[inodekey(key.ino)]].directory) ∧ (key.data? → fs0[ri0[key]].data? ∧ inodekey(key.ino) ∈ ri0 ∧ ¬ fs0[ri0[inodekey(key.ino)]].directory ∧ # fs0[ri0[key]].data = VFS_PAGE_SIZE), key = inodekey(m) ∨ key = dentrykey(m0, str0) ∨ key ≠ dentrykey(m, str) ∧ key ∈ ri0, ¬ boolvar0 ∧ ¬ boolvar2 ∨ boolvar0 ∧ boolvar2 ∧ m4 = m10, m6 ≠ 0 ∨ m0 = ROOT_INO, m2 ≠ 0 ∨ m = ROOT_INO ⊦ key.ino = 0, adr1 = adr2, adr1 = adr3, adr1 = adr4, adr2 = adr3, adr2 = adr4, adr3 = adr4, key = inodekey(m0), key = inodekey(m), m = 0, m0 = 0, m0 = m, adr4 ∈ (ri0 -- dentrykey(m, str))[dentrykey(m0, str0), adr2][inodekey(m), adr3], adr2 ∈ ri0 -- dentrykey(m, str), adr4 ∈ fs0, adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0, inodekey(m0) ∈ ro, dentrykey(m0, str0) ∈ ri0, inodekey(m) ∈ ro, adr3 ∈ (ri0 -- dentrykey(m, str))[dentrykey(m0, str0), adr2], ( (inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) = adr4 ∨ (inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) = adr3 ∨ (inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) = adr2 ∨ (inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) = adr1 ∨ (inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ∈ fs0) ∧ (adr4 = (inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ⊃ inodenode(inodekey(m0), md0, true, m6, m7 + (boolvar2 ⊃ 1;0), m8 + 1) ;(adr3 = (inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ⊃ inodenode(inodekey(m), md, true, m2, n0, m1) ;(adr2 = (inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ⊃ dentrynode(dentrykey(m0, str0), m3) ;(adr1 = (inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ⊃ dentrynode(dentrykey(m, str), 0) ;fs0[(inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key])))] ) ) ) ) .key = key ∧ ( key.inode? → (adr4 = (inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ⊃ inodenode(inodekey(m0), md0, true, m6, m7 + (boolvar2 ⊃ 1;0), m8 + 1) ;(adr3 = (inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ⊃ inodenode(inodekey(m), md, true, m2, n0, m1) ;(adr2 = (inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ⊃ dentrynode(dentrykey(m0, str0), m3) ;(adr1 = (inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ⊃ dentrynode(dentrykey(m, str), 0) ;fs0[(inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key])))] ) ) ) ) .inode?) ∧ ( key.dentry? → (adr4 = (inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ⊃ inodenode(inodekey(m0), md0, true, m6, m7 + (boolvar2 ⊃ 1;0), m8 + 1) ;(adr3 = (inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ⊃ inodenode(inodekey(m), md, true, m2, n0, m1) ;(adr2 = (inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ⊃ dentrynode(dentrykey(m0, str0), m3) ;(adr1 = (inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ⊃ dentrynode(dentrykey(m, str), 0) ;fs0[(inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key])))] ) ) ) ) .dentry? ∧ inodekey(key.ino) ∈ ri0 ∧ ( (adr4 = (inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ⊃ inodenode(inodekey(m0), md0, true, m6, m7 + (boolvar2 ⊃ 1;0), m8 + 1) ;(adr3 = (inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ⊃ inodenode(inodekey(m), md, true, m2, n0, m1) ;(adr2 = (inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ⊃ dentrynode(dentrykey(m0, str0), m3) ;(adr1 = (inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ⊃ dentrynode(dentrykey(m, str), 0) ;fs0[(inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key])))] ) ) ) ) .ino = m0 ∨ (adr4 = (inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ⊃ inodenode(inodekey(m0), md0, true, m6, m7 + (boolvar2 ⊃ 1;0), m8 + 1) ;(adr3 = (inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ⊃ inodenode(inodekey(m), md, true, m2, n0, m1) ;(adr2 = (inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ⊃ dentrynode(dentrykey(m0, str0), m3) ;(adr1 = (inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ⊃ dentrynode(dentrykey(m, str), 0) ;fs0[(inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key])))] ) ) ) ) .ino = m ∨ inodekey ((adr4 = (inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ⊃ inodenode(inodekey(m0), md0, true, m6, m7 + (boolvar2 ⊃ 1;0), m8 + 1) ;(adr3 = (inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ⊃ inodenode(inodekey(m), md, true, m2, n0, m1) ;(adr2 = (inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ⊃ dentrynode(dentrykey(m0, str0), m3) ;(adr1 = (inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ⊃ dentrynode(dentrykey(m, str), 0) ;fs0[(inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key])))] ) ) ) ) .ino) ∈ ri0) ∧ ¬ inodekey(key.ino) ∈ ro ∧ ¬ inodekey ((adr4 = (inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ⊃ inodenode(inodekey(m0), md0, true, m6, m7 + (boolvar2 ⊃ 1;0), m8 + 1) ;(adr3 = (inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ⊃ inodenode(inodekey(m), md, true, m2, n0, m1) ;(adr2 = (inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ⊃ dentrynode(dentrykey(m0, str0), m3) ;(adr1 = (inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ⊃ dentrynode(dentrykey(m, str), 0) ;fs0[(inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key])))] ) ) ) ) .ino) ∈ ro ∧ (adr4 = (m0 = key.ino ⊃ adr4;(m = key.ino ⊃ adr3;ri0[inodekey(key.ino)])) ⊃ inodenode(inodekey(m0), md0, true, m6, m7 + (boolvar2 ⊃ 1;0), m8 + 1) ;(adr3 = (m0 = key.ino ⊃ adr4;(m = key.ino ⊃ adr3;ri0[inodekey(key.ino)])) ⊃ inodenode(inodekey(m), md, true, m2, n0, m1) ;(adr2 = (m0 = key.ino ⊃ adr4;(m = key.ino ⊃ adr3;ri0[inodekey(key.ino)])) ⊃ dentrynode(dentrykey(m0, str0), m3) ;(adr1 = (m0 = key.ino ⊃ adr4;(m = key.ino ⊃ adr3;ri0[inodekey(key.ino)])) ⊃ dentrynode(dentrykey(m, str), 0) ;fs0[(m0 = key.ino ⊃ adr4;(m = key.ino ⊃ adr3;ri0[inodekey(key.ino)]))] ) ) ) ) .directory) ∧ ( key.data? → (adr4 = (inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ⊃ inodenode(inodekey(m0), md0, true, m6, m7 + (boolvar2 ⊃ 1;0), m8 + 1) ;(adr3 = (inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ⊃ inodenode(inodekey(m), md, true, m2, n0, m1) ;(adr2 = (inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ⊃ dentrynode(dentrykey(m0, str0), m3) ;(adr1 = (inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ⊃ dentrynode(dentrykey(m, str), 0) ;fs0[(inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key])))] ) ) ) ) .data? ∧ inodekey(key.ino) ∈ ri0 ∧ ¬ (adr4 = (m0 = key.ino ⊃ adr4;(m = key.ino ⊃ adr3;ri0[inodekey(key.ino)])) ⊃ inodenode(inodekey(m0), md0, true, m6, m7 + (boolvar2 ⊃ 1;0), m8 + 1) ;(adr3 = (m0 = key.ino ⊃ adr4;(m = key.ino ⊃ adr3;ri0[inodekey(key.ino)])) ⊃ inodenode(inodekey(m), md, true, m2, n0, m1) ;(adr2 = (m0 = key.ino ⊃ adr4;(m = key.ino ⊃ adr3;ri0[inodekey(key.ino)])) ⊃ dentrynode(dentrykey(m0, str0), m3) ;(adr1 = (m0 = key.ino ⊃ adr4;(m = key.ino ⊃ adr3;ri0[inodekey(key.ino)])) ⊃ dentrynode(dentrykey(m, str), 0) ;fs0[(m0 = key.ino ⊃ adr4;(m = key.ino ⊃ adr3;ri0[inodekey(key.ino)]))] ) ) ) ) .directory ∧ # (adr4 = (inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ⊃ inodenode(inodekey(m0), md0, true, m6, m7 + (boolvar2 ⊃ 1;0), m8 + 1) ;(adr3 = (inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ⊃ inodenode(inodekey(m), md, true, m2, n0, m1) ;(adr2 = (inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ⊃ dentrynode(dentrykey(m0, str0), m3) ;(adr1 = (inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ⊃ dentrynode(dentrykey(m, str), 0) ;fs0[(inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key])))] ) ) ) ) .data = VFS_PAGE_SIZE)

Rule argument

fma: key = inodekey(m)

Additional information

Used simplifier rules: ⊦ inodekey(m) = inodekey(m0) ↔ m = m0; (s)% ⊦ inodekey(m).ino = m; (s)% ⊦ inodekey(m).inode?; (s)% ⊦ ¬ inodekey(m).dentry?; (s)% ⊦ ¬ inodekey(m).data?; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).key = key; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).inode?; (s) Used formulas: key = inodekey(m)