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Proof step 439 from proof inv-rename-overwrite-keep-parent (previous step)

¬ boolvar1 ↔ ¬ boolvar0, fs0[ri0[inodekey(m1)]] = inodenode(key3, md3, boolvar1, m8 + 1, m11, m12), fs0[ri0[dentrykey(m, str0)]] = dentrynode(key4, m1), fs0[ri0[dentrykey(m, str)]] = dentrynode(key0, m2), fs0[ri0[inodekey(m2)]] = inodenode(key1, md0, boolvar0, m5, m9, m10), 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-cons(ri0, fs0), ri-inj(fi), ri-inj(ri0), ubifs-cons(fs0, ri0, ro, fi, fo, log0), dentrykey(m, str) ∈ ri0, inodekey(m2) ∈ ri0, dentrykey(m, str0) ∈ ri0, inodekey(m1) ∈ ri0, ri0[dentrykey(m, str)] ∈ fs0, ri0[inodekey(m2)] ∈ fs0, inodekey(m) ∈ ri0, ri0[dentrykey(m, str0)] ∈ fs0, ri0[inodekey(m1)] ∈ fs0, ri0[inodekey(m)] ∈ fs0, boolvar1 → dentrykeys(inodekey(m1), ri0) = ∅, m4 ≠ 0 ∨ m = ROOT_INO, ¬ boolvar0 ∧ ¬ boolvar3 ∨ boolvar0 ∧ boolvar3 ∧ m3 = m10, ¬ boolvar0 ∧ ¬ boolvar2 ∨ boolvar1 ∧ boolvar2 ∧ m6 = m12 ⊦ adr1 = adr2, adr1 = adr3, adr1 = adr4, adr2 = adr3, adr2 = adr4, adr3 = adr4, m = 0, m1 = ROOT_INO, m1 = 0, m8 = 0, mkdentry(str, m2) = mkdentry(str0, m1), orphans-cons (fs0[adr1, dentrynode(dentrykey(m, str), 0)][adr2, dentrynode(dentrykey(m, str0), m2)][adr3, inodenode(inodekey(m), md, true, m4, n0, m0)] [adr4, inodenode(inodekey(m1), md1, boolvar2, m8, m11, m6) ], (ri0 -- dentrykey(m, str))[dentrykey(m, str0), adr2][inodekey(m), adr3][inodekey(m1), adr4], ro), adr4 ∈ (ri0 -- dentrykey(m, str))[dentrykey(m, str0), adr2][inodekey(m), adr3], adr2 ∈ ri0 -- dentrykey(m, str), adr4 ∈ fs0, adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0, inodekey(m) ∈ ro, adr3 ∈ (ri0 -- dentrykey(m, str))[dentrykey(m, str0), adr2]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 440:
¬ boolvar1 ↔ ¬ boolvar0, fs0[ri0[inodekey(ino)]].nlink = 0 ∧ ino ≠ ROOT_INO ↔ inodekey(ino) ∈ ro, fs0[ri0[inodekey(m2)]] = inodenode(key1, md0, boolvar0, m5, m9, m10), fs0[ri0[dentrykey(m, str)]] = dentrynode(key0, m2), fs0[ri0[dentrykey(m, str0)]] = dentrynode(key4, m1), fs0[ri0[inodekey(m1)]] = inodenode(key3, md3, boolvar1, m8 + 1, m11, m12), 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-cons(ri0, fs0), ri-inj(ri0), ri-inj(fi), ubifs-cons(fs0, ri0, ro, fi, fo, log0), ri0[inodekey(m)] ∈ fs0, ri0[inodekey(m1)] ∈ fs0, ri0[dentrykey(m, str0)] ∈ fs0, inodekey(m) ∈ ri0, ri0[inodekey(m2)] ∈ fs0, ri0[dentrykey(m, str)] ∈ fs0, inodekey(m1) ∈ ri0, dentrykey(m, str0) ∈ ri0, inodekey(m2) ∈ ri0, dentrykey(m, str) ∈ ri0, inodekey(ino) ∈ ri0, boolvar1 → dentrykeys(inodekey(m1), ri0) = ∅, ¬ boolvar0 ∧ ¬ boolvar2 ∨ boolvar1 ∧ boolvar2 ∧ m6 = m12, ¬ boolvar0 ∧ ¬ boolvar3 ∨ boolvar0 ∧ boolvar3 ∧ m3 = m10, m4 ≠ 0 ∨ m = ROOT_INO ⊦ (adr4 = (m1 = ino ⊃ adr4;(m = ino ⊃ adr3;ri0[inodekey(ino)])) ⊃ inodenode(inodekey(m1), md1, boolvar2, m8, m11, m6) ;(adr3 = (m1 = ino ⊃ adr4;(m = ino ⊃ adr3;ri0[inodekey(ino)])) ⊃ inodenode(inodekey(m), md, true, m4, n0, m0) ;(adr2 = (m1 = ino ⊃ adr4;(m = ino ⊃ adr3;ri0[inodekey(ino)])) ⊃ dentrynode(dentrykey(m, str0), m2) ;(adr1 = (m1 = ino ⊃ adr4;(m = ino ⊃ adr3;ri0[inodekey(ino)])) ⊃ dentrynode(dentrykey(m, str), 0) ;fs0[(m1 = ino ⊃ adr4;(m = ino ⊃ adr3;ri0[inodekey(ino)]))] ) ) ) ) .nlink = 0 ∧ ino ≠ ROOT_INO ↔ inodekey(ino) ∈ ro, adr1 = adr4, adr1 = adr3, adr1 = adr2, adr2 = adr4, adr2 = adr3, adr3 = adr4, m = 0, m1 = 0, m1 = ROOT_INO, m8 = 0, mkdentry(str, m2) = mkdentry(str0, m1), adr3 ∈ (ri0 -- dentrykey(m, str))[dentrykey(m, str0), adr2], inodekey(m) ∈ ro, adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0, adr4 ∈ fs0, adr2 ∈ ri0 -- dentrykey(m, str), adr4 ∈ (ri0 -- dentrykey(m, str))[dentrykey(m, str0), adr2][inodekey(m), adr3]

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)%⊦ orphans-cons(fs, ri, ro) → ( orphans-cons(fs0, ri0, ro0) ↔ (∀ ino. ( inodekey(ino) ∈ ri → ( fs[ri[inodekey(ino)]].nlink = 0 ∧ ino ≠ ROOT_INO ↔ inodekey(ino) ∈ ro)) → inodekey(ino) ∈ ri0 → ( fs0[ri0[inodekey(ino)]].nlink = 0 ∧ ino ≠ ROOT_INO ↔ inodekey(ino) ∈ ro0))); (ss)