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Proof step 75 from proof inv-write-inode (previous step)

fs0[ri[inodekey(m)]].nlink = 0 ∧ m ≠ ROOT_INO ↔ inodekey(m) ∈ ro, fs0[ri[inodekey(ino)]].nlink = 0 ∧ ino ≠ ROOT_INO ↔ inodekey(ino) ∈ ro, fs0[ri[inodekey(m)]].inode?, fo.inodes?, ro.inodes?, file-node-cons(fs0, ri), log-cons(log0, fs0), orphans-cons(fs0, ri, ro), replay-cons-strong(fs0, ri, ro, fi, fo, log0), ri-inj(fi), ri-inj(ri), ubifs-cons(fs0, ri, ro, fi, fo, log0), ri[inodekey(m)] ∈ fs0, inodekey(m) ∈ ri, inodekey(ino) ∈ ri, ¬ fs0[ri[inodekey(m)]].directory ∧ ¬ boolvar0 ∨ fs0[ri[inodekey(m)]].directory ∧ boolvar0 ∧ m2 = fs0[ri[inodekey(m)]].size ⊦ (adr1 = (m = ino ⊃ adr1;ri[inodekey(ino)]) ⊃ inodenode(inodekey(m), md, boolvar0, fs0[ri[inodekey(m)]].nlink, fs0[ri[inodekey(m)]].nsubdirs, m2) ;fs0[(m = ino ⊃ adr1;ri[inodekey(ino)])] ) .nlink = 0 ∧ ino ≠ ROOT_INO ↔ inodekey(ino) ∈ ro, adr1 ∈ fs0

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 76:
fs0[ri[inodekey(ino)]].nlink = 0 ∧ ino ≠ ROOT_INO ↔ inodekey(ino) ∈ ro, m0 = 0 ∧ m ≠ ROOT_INO ↔ inodekey(m) ∈ ro, fs0[ri[inodekey(m)]] = inodenode(key, md0, boolvar, m0, m1, m3), fs0[ri[inodekey(m)]].inode?, ro.inodes?, fo.inodes?, file-node-cons(fs0, ri), log-cons(log0, fs0), orphans-cons(fs0, ri, ro), replay-cons-strong(fs0, ri, ro, fi, fo, log0), ri-inj(ri), ri-inj(fi), ubifs-cons(fs0, ri, ro, fi, fo, log0), inodekey(ino) ∈ ri, inodekey(m) ∈ ri, ri[inodekey(m)] ∈ fs0, ¬ boolvar ∧ ¬ boolvar0 ∨ boolvar ∧ boolvar0 ∧ m2 = m3 ⊦ (adr1 = (m = ino ⊃ adr1;ri[inodekey(ino)]) ⊃ inodenode(inodekey(m), md, boolvar0, m0, m1, m2);fs0[(m = ino ⊃ adr1;ri[inodekey(ino)])]).nlink = 0 ∧ ino ≠ ROOT_INO ↔ inodekey(ino) ∈ ro, adr1 ∈ fs0

Rule argument

spec: node name: elim-03 seq: ⊦ nd.inode? → ( ( ( ( (key = nd.key ∧ md = nd.meta) ∧ (boolvar ↔ nd.directory)) ∧ m = nd.nlink) ∧ m0 = nd.nsubdirs) ∧ m1 = nd.size ↔ nd = inodenode(key, md, boolvar, m, m0, m1)) subst: [nd, key, md, boolvar, m, m0, m1] → [fs0[ri[inodekey(m)]], key, md0, boolvar, m0, m1, m3]

Additional information

Used simplifier rules: ⊦ nd.inode? → ( ( ( ( (key = nd.key ∧ md = nd.meta) ∧ (boolvar ↔ nd.directory)) ∧ m = nd.nlink) ∧ m0 = nd.nsubdirs) ∧ m1 = nd.size ↔ nd = inodenode(key, md, boolvar, m, m0, m1)); (elim) Used terms: fs0[ri[inodekey(m)]], key, md0, boolvar, m0, m1, m3