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Proof step 111 from proof inv-mkdir (previous step)

fs1[ri1[inodekey(m)]].directory, fs1[ri1[inodekey(m)]].inode?, fo.inodes?, ro.inodes?, file-node-cons(fs1, ri1), log-cons(log0, fs1), orphans-cons(fs1, ri1, ro), replay-cons-strong(fs1, ri1, ro, fi, fo, log0), ri-inj(fi), ri-inj(ri1), ubifs-cons(fs1, ri1, ro, fi, fo, log0), ri1[inodekey(m)] ∈ fs1, inodekey(m) ∈ ri1, fs1[ri1[inodekey(m)]].nlink ≠ 0 ∨ m = ROOT_INO ⊦ adr1 = adr3, adr1 = adr2, adr2 = adr3, n = 0, file-node-cons (fs1[adr1, inodenode(inodekey(m), md0, true, fs1[ri1[inodekey(m)]].nlink, fs1[ri1[inodekey(m)]].nsubdirs + 1, fs1[ri1[inodekey(m)]].size + 1)] [adr2, dentrynode(dentrykey(m, str), n) ] [adr3, inodenode(inodekey(n), md, true, 1, 0, 0) ], ri1[inodekey(m), adr1][dentrykey(m, str), adr2][inodekey(n), adr3]), inodekey(m) ∈ ro, dentrykey(m, str) ∈ ri1, inodekey(n) ∈ fo, inodekey(n) ∈ ri1, adr1 ∈ fs1, adr2 ∈ fs1, adr3 ∈ fs1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 112:
fs1[ri1[inodekey(m)]].directory, fs1[ri1[inodekey(m)]].inode?, fo.inodes?, ro.inodes?, file-node-cons(fs1, ri1), log-cons(log0, fs1), orphans-cons(fs1, ri1, ro), replay-cons-strong(fs1, ri1, ro, fi, fo, log0), ri-inj(fi), ri-inj(ri1), ubifs-cons(fs1, ri1, ro, fi, fo, log0), ri1[inodekey(m)] ∈ fs1, inodekey(m) ∈ ri1, inodekey(ino) ∈ ri1, ¬ fs1[ri1[inodekey(ino)]].directory → fs1[ri1[inodekey(ino)]].nsubdirs = 0, fs1[ri1[inodekey(m)]].nlink ≠ 0 ∨ m = ROOT_INO ⊦ (adr3 = (m = ino ⊃ adr1;ri1[inodekey(ino)]) ⊃ inodenode(inodekey(n), md, true, 1, 0, 0) ;(adr2 = (m = ino ⊃ adr1;ri1[inodekey(ino)]) ⊃ dentrynode(dentrykey(m, str), n) ;(adr1 = (m = ino ⊃ adr1;ri1[inodekey(ino)]) ⊃ inodenode(inodekey(m), md0, true, fs1[ri1[inodekey(m)]].nlink, fs1[ri1[inodekey(m)]].nsubdirs + 1, fs1[ri1[inodekey(m)]].size + 1) ;fs1[(m = ino ⊃ adr1;ri1[inodekey(ino)])] ) ) ) .nsubdirs = 0, adr1 = adr3, adr1 = adr2, adr2 = adr3, n = 0, (adr3 = (m = ino ⊃ adr1;ri1[inodekey(ino)]) ⊃ inodenode(inodekey(n), md, true, 1, 0, 0) ;(adr2 = (m = ino ⊃ adr1;ri1[inodekey(ino)]) ⊃ dentrynode(dentrykey(m, str), n) ;(adr1 = (m = ino ⊃ adr1;ri1[inodekey(ino)]) ⊃ inodenode(inodekey(m), md0, true, fs1[ri1[inodekey(m)]].nlink, fs1[ri1[inodekey(m)]].nsubdirs + 1, fs1[ri1[inodekey(m)]].size + 1) ;fs1[(m = ino ⊃ adr1;ri1[inodekey(ino)])] ) ) ) .directory, inodekey(m) ∈ ro, dentrykey(m, str) ∈ ri1, inodekey(n) ∈ fo, inodekey(n) ∈ ri1, adr1 ∈ fs1, adr2 ∈ fs1, adr3 ∈ fs1

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-fs: ⊦ fs[adr0, nd][adr1] = (adr0 = adr1 ⊃ nd;fs[adr1]);% ⊦ inodenode(key, md, boolvar, m, m0, m1).nsubdirs = m0; (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)