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Proof step 1065 from proof refine-rename-overwrite-keep-parent-different (previous step)

¬ fs0[ri0[inodekey(m3)]].directory ↔ ¬ fs0[ri0[inodekey(m)]].directory, abs-dirs(fs0, ri0)[m7] = mkdir(0, md, m9, m12, entries), fs0[ri0[inodekey(m7)]] = inodenode(key1, md2, true, m4, n0 + (boolvar1 ⊃ 1;0), m11 + 1), fs0[ri0[dentrykey(m7, str)]] = dentrynode(key2, m), fs0[ri0[dentrykey(m7, str0)]] = dentrynode(key0, m3), orphans(fs0, ri0).inodes?, fo.inodes?, afs-cons(abs-dirs(fs0, ri0), abs-files(fs0, ri0)), file-node-cons (fs0[adr1, dentrynode(dentrykey(m7, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)][adr3, inodenode(inodekey(m7), md1, true, m4, n0, m11)] [adr4, inodenode(inodekey(m3), md0, boolvar2, m10, m5, m6) ], (ri0 -- dentrykey(m7, str))[dentrykey(m7, str0), adr2][inodekey(m7), adr3][inodekey(m3), adr4]), file-node-cons(fs0, ri0), log-cons (log0, fs0[adr1, dentrynode(dentrykey(m7, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)][adr3, inodenode(inodekey(m7), md1, true, m4, n0, m11)] [adr4, inodenode(inodekey(m3), md0, boolvar2, m10, m5, m6) ]), log-cons(log0, fs0), orphans-cons (fs0[adr1, dentrynode(dentrykey(m7, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)][adr3, inodenode(inodekey(m7), md1, true, m4, n0, m11)] [adr4, inodenode(inodekey(m3), md0, boolvar2, m10, m5, m6) ], (ri0 -- dentrykey(m7, str))[dentrykey(m7, str0), adr2][inodekey(m7), adr3][inodekey(m3), adr4], orphans(fs0, ri0)), orphans-cons(fs0, ri0, orphans(fs0, ri0)), replay-cons-strong (fs0[adr1, dentrynode(dentrykey(m7, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)][adr3, inodenode(inodekey(m7), md1, true, m4, n0, m11)] [adr4, inodenode(inodekey(m3), md0, boolvar2, m10, m5, m6) ], (ri0 -- dentrykey(m7, str))[dentrykey(m7, str0), adr2][inodekey(m7), adr3][inodekey(m3), adr4], orphans(fs0, ri0), fi, fo, (((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 '), replay-cons-strong(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), ri-cons(ri0, fs0), ri-inj((ri0 -- dentrykey(m7, str))[dentrykey(m7, str0), adr2][inodekey(m7), adr3][inodekey(m3), adr4]), ri-inj(fi), ri-inj(ri0), ubifs-cons (fs0[adr1, dentrynode(dentrykey(m7, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)][adr3, inodenode(inodekey(m7), md1, true, m4, n0, m11)] [adr4, inodenode(inodekey(m3), md0, boolvar2, m10, m5, m6) ], (ri0 -- dentrykey(m7, str))[dentrykey(m7, str0), adr2][inodekey(m7), adr3][inodekey(m3), adr4], orphans(fs0, ri0), fi, fo, (((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 '), ubifs-cons(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), inodekey(m) ∈ ri0, inodekey(m3) ∈ ri0, dentrykey(m7, str) ∈ ri0, dentrykey(m7, str0) ∈ ri0, inodekey(m7) ∈ ri0, ri0[dentrykey(m7, str0)] ∈ fs0, ri0[inodekey(m7)] ∈ fs0, ri0[dentrykey(m7, str)] ∈ fs0, boolvar3 → boolvar4, fs0[ri0[inodekey(m3)]].directory → abs-children(m3, fs0, ri0) = ∅, fs0[ri0[inodekey(m3)]].directory → dentrykeys(inodekey(m3), ri0) = ∅, m4 ≠ 0 ∨ m7 = ROOT_INO, links(m7, abs-dirs(fs0, ri0)) ≠ ∅ ∨ m7 = ROOT_INO, ¬ fs0[ri0[inodekey(m)]].directory ∧ ¬ boolvar1 ∧ m0 = fs0[ri0[inodekey(m)]].nlink ∧ m1 = fs0[ri0[inodekey(m)]].nsubdirs ∨ fs0[ri0[inodekey(m)]].directory ∧ boolvar1 ∧ m0 = fs0[ri0[inodekey(m)]].nlink ∧ m1 = fs0[ri0[inodekey(m)]].nsubdirs ∧ m2 = fs0[ri0[inodekey(m)]].size, ¬ fs0[ri0[inodekey(m)]].directory ∧ ¬ boolvar2 ∧ m10 + 1 = fs0[ri0[inodekey(m3)]].nlink ∧ m5 = fs0[ri0[inodekey(m3)]].nsubdirs ∨ fs0[ri0[inodekey(m3)]].directory ∧ boolvar2 ∧ m10 + 1 = fs0[ri0[inodekey(m3)]].nlink ∧ m5 = fs0[ri0[inodekey(m3)]].nsubdirs ∧ m6 = fs0[ri0[inodekey(m3)]].size, fs0[ri0[inodekey(m)]].directory ∧ m0 = fs0[ri0[inodekey(m)]].nlink ∧ m2 = fs0[ri0[inodekey(m)]].size ∧ m1 = fs0[ri0[inodekey(m)]].nsubdirs ∧ boolvar1 ∨ ¬ fs0[ri0[inodekey(m)]].directory ∧ m0 = fs0[ri0[inodekey(m)]].nlink ∧ m1 = 0 ∧ ¬ boolvar1, fs0[ri0[inodekey(m3)]].directory ∧ m10 + 1 = fs0[ri0[inodekey(m3)]].nlink ∧ m6 = fs0[ri0[inodekey(m3)]].size ∧ m5 = fs0[ri0[inodekey(m3)]].nsubdirs ∧ boolvar2 ∨ ¬ fs0[ri0[inodekey(m)]].directory ∧ m10 + 1 = fs0[ri0[inodekey(m3)]].nlink ∧ m5 = 0 ∧ ¬ boolvar2 ⊦ adr1 = adr4, adr1 = adr3, adr1 = adr2, adr2 = adr4, adr2 = adr3, adr3 = adr4, m10 = 0, m3 = 0, m3 = ROOT_INO, m7 = 0, mkdentry(str, m) = mkdentry(str0, m3), adr3 ∈ (ri0 -- dentrykey(m7, str))[dentrykey(m7, str0), adr2], adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0, adr4 ∈ fs0, adr2 ∈ ri0 -- dentrykey(m7, str), adr4 ∈ (ri0 -- dentrykey(m7, str))[dentrykey(m7, str0), adr2][inodekey(m7), adr3], m4 = 0 ∧ m7 ≠ ROOT_INO

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: aubifs-abs name: at-dirs seq: ⊦ inodekey(ino) ∈ ri ∧ fs[ri[inodekey(ino)]].directory → abs-dirs(fs, ri)[ino] = abs-dir(ino, fs, ri) subst: [ino, ri, fs] → [m7, ri0, fs0] flags: <all paths>

Additional information

Used simplifier rules: ⊦ abs-dir(ino, fs, ri) = mkdir (fs[ri[inodekey(ino)]].size, fs[ri[inodekey(ino)]].meta, fs[ri[inodekey(ino)]].nlink, fs[ri[inodekey(ino)]].nsubdirs, abs-children(ino, fs, ri)); (s)%⊦ mkdir(m, md, m0, m1, entries) = mkdir(m2, md0, m3, m4, entries0) ↔ m = m2 ∧ md = md0 ∧ m0 = m3 ∧ m1 = m4 ∧ entries = entries0; (ws)% ⊦ inodenode(key, md, boolvar, m, m0, m1).size = m1; (s)% ⊦ m + n = 0 ↔ m = 0 ∧ n = 0; (ws)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%⊦ dentrykey(ino, str) ∈ ri ∧ ubifs-cons(fs, ri, ro, fi, fo, log) → fs[ri[inodekey(ino)]].directory; (ss) Used terms: m7, ri0, fs0