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Proof step 114 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, inodekey(ino) ∈ ri1, ¬ fs1[ri1[inodekey(ino)]].directory → fs1[ri1[inodekey(ino)]].nsubdirs = 0, fs1[ri1[inodekey(m)]].nlink ≠ 0 ∨ m = ROOT_INO ⊦ (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, adr3 = (m = ino ⊃ adr1;ri1[inodekey(ino)]), n = 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

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 115:
fs1[ri1[inodekey(m)]].directory, fs1[ri1[inodekey(m)]].inode?, ro.inodes?, fo.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(ri1), ri-inj(fi), ubifs-cons(fs1, ri1, ro, fi, fo, log0), inodekey(ino) ∈ ri1, inodekey(m) ∈ ri1, ri1[inodekey(m)] ∈ fs1, ¬ fs1[ri1[inodekey(ino)]].directory → fs1[ri1[inodekey(ino)]].nsubdirs = 0, fs1[ri1[inodekey(m)]].nlink ≠ 0 ∨ m = ROOT_INO ⊦ (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 = adr2, adr1 = adr3, adr2 = adr3, adr3 = (m = ino ⊃ adr1;ri1[inodekey(ino)]), m = ino, n = 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, adr3 ∈ fs1, adr2 ∈ fs1, adr1 ∈ fs1, inodekey(n) ∈ ri1, inodekey(n) ∈ fo, dentrykey(m, str) ∈ ri1, inodekey(m) ∈ ro

Rule argument

fma: m = ino

Additional information

Used simplifier rules: ⊦ inodenode(key, md, boolvar, m, m0, m1).nsubdirs = m0; (s)% ⊦ m + 1 ≠ 0; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ inodenode(key, md, boolvar, m, m0, m1).directory ↔ boolvar; (s) Used formulas: m = ino