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Proof step 178 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, m2 ≠ 0 ∨ m = ROOT_INO, m6 ≠ 0 ∨ m0 = ROOT_INO, ¬ boolvar0 ∧ ¬ boolvar2 ∨ boolvar0 ∧ boolvar2 ∧ m4 = m10 ⊦ adr1 = adr4, adr1 = adr3, adr1 = adr2, adr2 = adr4, adr2 = adr3, adr3 = adr4, m = 0, m0 = m, m0 = 0, file-node-cons (fs0[adr1, dentrynode(dentrykey(m, str), 0)][adr2, dentrynode(dentrykey(m0, str0), m3)][adr3, inodenode(inodekey(m), md, true, m2, n0, m1)] [adr4, inodenode(inodekey(m0), md0, true, m6, m7 + (boolvar2 ⊃ 1;0), m8 + 1) ], (ri0 -- dentrykey(m, str))[dentrykey(m0, str0), adr2][inodekey(m), adr3][inodekey(m0), adr4]), 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]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 179:
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, inodekey(ino) ∈ ri0, ¬ fs0[ri0[inodekey(ino)]].directory → fs0[ri0[inodekey(ino)]].nsubdirs = 0, ¬ boolvar0 ∧ ¬ boolvar2 ∨ boolvar0 ∧ boolvar2 ∧ m4 = m10, m6 ≠ 0 ∨ m0 = ROOT_INO, m2 ≠ 0 ∨ m = ROOT_INO ⊦ (adr4 = (m0 = ino ⊃ adr4;(m = ino ⊃ adr3;ri0[inodekey(ino)])) ⊃ inodenode(inodekey(m0), md0, true, m6, m7 + (boolvar2 ⊃ 1;0), m8 + 1) ;(adr3 = (m0 = ino ⊃ adr4;(m = ino ⊃ adr3;ri0[inodekey(ino)])) ⊃ inodenode(inodekey(m), md, true, m2, n0, m1) ;(adr2 = (m0 = ino ⊃ adr4;(m = ino ⊃ adr3;ri0[inodekey(ino)])) ⊃ dentrynode(dentrykey(m0, str0), m3) ;(adr1 = (m0 = ino ⊃ adr4;(m = ino ⊃ adr3;ri0[inodekey(ino)])) ⊃ dentrynode(dentrykey(m, str), 0) ;fs0[(m0 = ino ⊃ adr4;(m = ino ⊃ adr3;ri0[inodekey(ino)]))] ) ) ) ) .nsubdirs = 0, adr1 = adr2, adr1 = adr3, adr1 = adr4, adr2 = adr3, adr2 = adr4, adr3 = adr4, m = 0, m0 = 0, m0 = m, (adr4 = (m0 = ino ⊃ adr4;(m = ino ⊃ adr3;ri0[inodekey(ino)])) ⊃ inodenode(inodekey(m0), md0, true, m6, m7 + (boolvar2 ⊃ 1;0), m8 + 1) ;(adr3 = (m0 = ino ⊃ adr4;(m = ino ⊃ adr3;ri0[inodekey(ino)])) ⊃ inodenode(inodekey(m), md, true, m2, n0, m1) ;(adr2 = (m0 = ino ⊃ adr4;(m = ino ⊃ adr3;ri0[inodekey(ino)])) ⊃ dentrynode(dentrykey(m0, str0), m3) ;(adr1 = (m0 = ino ⊃ adr4;(m = ino ⊃ adr3;ri0[inodekey(ino)])) ⊃ dentrynode(dentrykey(m, str), 0) ;fs0[(m0 = ino ⊃ adr4;(m = ino ⊃ adr3;ri0[inodekey(ino)]))] ) ) ) ) .directory, 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]

Rule argument

Additional information

Used simplifier rules: in-ri: ⊦ key0 ∈ ri[key1, adr] ↔ key0 = key1 ∨ key0 ∈ ri;%at-ri: ⊦ ri[key0, adr][key1] = (key0 = key1 ⊃ adr;ri[key1]);%at-del-ri: ⊦ (ri -- key0)[key1] = (key0 = key1 ⊃ (∅)[key0];ri[key1]);%at-fs: ⊦ fs[adr0, nd][adr1] = (adr0 = adr1 ⊃ nd;fs[adr1]);% ⊦ key ∈ ri -- key0 ↔ key ≠ key0 ∧ key ∈ ri; (s)% ⊦ inodekey(m) ≠ dentrykey(m0, str); (s)% ⊦ inodekey(m) = inodekey(m0) ↔ m = m0; (s)%⊦ file-node-cons(fs, ri) → ( file-node-cons(fs0, ri0) ↔ (∀ ino. ( inodekey(ino) ∈ ri ∧ ¬ fs[ri[inodekey(ino)]].directory → fs[ri[inodekey(ino)]].nsubdirs = 0) → inodekey(ino) ∈ ri0 ∧ ¬ fs0[ri0[inodekey(ino)]].directory → fs0[ri0[inodekey(ino)]].nsubdirs = 0)); (ss)