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Proof step 95 from proof inv-unlink (previous step)

fs0[ri0[inodekey(m1)]].size = m + 1, 1 = fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].nlink, links(fs0[ri0[dentrykey(m1, str)]].ino, fs0, ri0) = ∅ ++ dentrykey(m1, str), fs0[ri0[dentrykey(m1, str)]].dentry?, fs0[ri0[inodekey(m1)]].directory, fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].inode?, fs0[ri0[inodekey(m1)]].inode?, 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(m1, str) ∈ ri0, ri0[dentrykey(m1, str)] ∈ fs0, inodekey(fs0[ri0[dentrykey(m1, str)]].ino) ∈ ri0, ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)] ∈ fs0, inodekey(m1) ∈ ri0, ri0[inodekey(m1)] ∈ fs0, 1 ≤ fs0[ri0[inodekey(m1)]].size, fs0[ri0[inodekey(m1)]].nlink ≠ 0 ∨ m1 = ROOT_INO ⊦ fs0[ri0[dentrykey(m1, str)]].ino = ROOT_INO, fs0[ri0[dentrykey(m1, str)]].ino = 0, fs0[ri0[inodekey(m1)]].size = 0, adr1 = adr2, adr1 = adr3, adr2 = adr3, m1 = 0, fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].directory, replay-cons-strong (fs0[adr1, inodenode(inodekey(m1), md0, true, fs0[ri0[inodekey(m1)]].nlink, fs0[ri0[inodekey(m1)]].nsubdirs, m)] [adr2, dentrynode(dentrykey(m1, str), 0) ] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(m1, str)]].ino), md, false, 0, fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].nsubdirs, m2) ], (ri0[inodekey(m1), adr1] -- dentrykey(m1, str))[inodekey(fs0[ri0[dentrykey(m1, str)]].ino), adr3], ro ++ inodekey(fs0[ri0[dentrykey(m1, str)]].ino), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0, inodekey(fs0[ri0[dentrykey(m1, str)]].ino) ∈ ro, inodekey(m1) ∈ ro

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: at-fs: ⊦ fs[adr0, nd][adr1] = (adr0 = adr1 ⊃ nd;fs[adr1]);% ⊦ m ≤ m + n; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + 1 ≠ 0; (s)%not-zero: 0 < n ⊦ (* n) ≤ m → m ≠ 0; (forward) from specification nat% ⊦ replay-log(adr ', fs, ri) = replay-one(adr, fs[adr], ri); (s)%⊦ replay-log(adr ' + log, fs, ri) = replay-log(log, fs, replay-one(adr, fs[adr], ri)); (s)%⊦ replay(ax0 + ax1, fs, fi, fo) = replay-log(ax1, fs, replay(ax0, fs, fi, fo)); (s)%a: ⊦ (ax + ax0) + ax1 = ax + ax0 + ax1; from specification list[address-list-set]%⊦ replay-safe(adr ', fs, ri) ↔ adr ∈ fs ∧ ¬ adr ∈ ri ∧ node-cons(fs[adr].key, fs[adr]); (s)%⊦ replay-one(adr, dentrynode(key, ino), ri) = (ino ≠ 0 ⊃ ri[key, adr];ri -- key); (s)% ⊦ dentrykey(m, str).dentry?; (s)% ⊦ node-cons(key0, dentrynode(key1, ino)) ↔ key0.dentry?; (s)% ⊦ dentrynode(key, m).key = key; (s)%⊦ replay-one(adr, inodenode(key, md, boolvar, n, n0, m), ri) = (n ≠ 0 ∨ key.ino = ROOT_INO ⊃ ri[key, adr] ;(boolvar ⊃ ri -- key;ri ⊖ key) ); (s)% ⊦ inodekey(m).ino = m; (s)% ⊦ inodekey(m).inode?; (s)%⊦ node-cons(key0, inodenode(key1, md, boolvar, n, n0, m)) ↔ key0.inode? ∧ key0.ino ≠ 0; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).key = key; (s)% ⊦ adr ≠ adr0 → fs[adr0, nd][adr] = fs[adr]; (s)% ⊦ adr ∈ fs[adr1, nd] ↔ adr = adr1 ∨ adr ∈ fs; (s)% ⊦ adr ≠ adr0 → (adr ∈ fs[adr0, nd] ↔ adr ∈ fs); (s)%⊦ replay-safe(adr ' + log, fs, ri) ↔ adr ∈ fs ∧ ¬ adr ∈ ri ∧ node-cons(fs[adr].key, fs[adr]) ∧ replay-safe(log, fs, replay-one(adr, fs[adr], ri)); (s)%⊦ replay-safe(log0 + log1, fs, ri) ↔ replay-safe(log0, fs, ri) ∧ replay-safe(log1, fs, replay-log(log0, fs, ri)); (s)% ⊦ replay(log, fs, fi, fo) = replay-log(log, fs, fi ⊖ fo); (s)%⊦ replay-cons-strong(fs, ri, ro, fi, fo, log) → ( replay-cons-strong(fs0, ri0, ro0, fi0, fo0, log0) ↔ replay-safe(log, fs, fi ⊖ fo) ∧ replay(log, fs, fi, fo) = ri ⊖ ro → replay-safe(log0, fs0, fi0 ⊖ fo0) ∧ replay(log0, fs0, fi0, fo0) = ri0 ⊖ ro0); (ss)