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Proof step 117 from proof refine-write-inode (previous step)

fs0[ri[inodekey(m)]] = inodenode(key, md0, false, m0, 0, m3), abs-dirs(fs0[adr1, inodenode(inodekey(m), md, false, m0, 0, m2)], ri[inodekey(m), adr1])[ino] ≠ mkdir (fs0[ri[inodekey(ino)]].size, fs0[ri[inodekey(ino)]].meta, fs0[ri[inodekey(ino)]].nlink, fs0[ri[inodekey(ino)]].nsubdirs, abs-children(ino, fs0, ri)), adr1 ≠ ri[inodekey(ino)], ino ≠ m, m ≠ 0, fs0[ri[inodekey(ino)]].directory, orphans(fs0, ri).inodes?, fo.inodes?, afs-cons(abs-dirs(fs0, ri), abs-files(fs0, ri)), afs-cons(abs-dirs(fs0, ri), abs-files(fs0, ri)[m, mkfile(m2, md, m0, abs-content(m, fs0, ri))]), file-node-cons(fs0, ri), log-cons(log0, fs0), orphans-cons(fs0, ri, orphans(fs0, ri)), replay-cons-strong(fs0, ri, orphans(fs0, ri), fi, fo, log0), ri-cons(ri, fs0), ri-inj(ri), ri-inj(fi), ubifs-cons(fs0, ri, orphans(fs0, ri), fi, fo, log0), inodekey(ino) ∈ ri, inodekey(m) ∈ ri, ri[inodekey(m)] ∈ fs0, ¬ adr1 ∈ fs0, asynced0 → boolvar1 ⊦ ∃ err0. ⌊err0⌋ ∧ ⟨err := err0; asynced0 := ?⟩ ( abs-dirs(fs0, ri) = abs-dirs(fs0[adr1, inodenode(inodekey(m), md, false, m0, 0, m2)], ri[inodekey(m), adr1]) ∧ abs-files(fs0, ri) = abs-files(fs0[adr1, inodenode(inodekey(m), md, false, m0, 0, m2)], ri[inodekey(m), adr1]) ∧ orphans(fs0[adr1, inodenode(inodekey(m), md, false, m0, 0, m2)], ri[inodekey(m), adr1]) = orphans(fs0, ri) ∧ (asynced0 → boolvar) ∧ ESUCCESS = err)

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 118:
⊦ inodekey(ino) ∈ ri ∧ fs[ri[inodekey(ino)]].directory → abs-dirs(fs, ri)[ino] = abs-dir(ino, fs, ri)
Proof step 119:
fs0[ri[inodekey(m)]] = inodenode(key, md0, false, m0, 0, m3), fs0[ri[inodekey(ino)]].directory, fs0[adr1, inodenode(inodekey(m), md, false, m0, 0, m2)][ri[inodekey(m), adr1][inodekey(ino)]].directory, fo.inodes?, orphans(fs0, ri).inodes?, afs-cons(abs-dirs(fs0, ri), abs-files(fs0, ri)[m, mkfile(m2, md, m0, abs-content(m, fs0, ri))]), afs-cons(abs-dirs(fs0, ri), abs-files(fs0, ri)), file-node-cons(fs0, ri), log-cons(log0, fs0), orphans-cons(fs0, ri, orphans(fs0, ri)), replay-cons-strong(fs0, ri, orphans(fs0, ri), fi, fo, log0), ri-cons(ri, fs0), ri-inj(fi), ri-inj(ri), ubifs-cons(fs0, ri, orphans(fs0, ri), fi, fo, log0), ri[inodekey(m)] ∈ fs0, inodekey(m) ∈ ri, inodekey(ino) ∈ ri, inodekey(ino) ∈ ri[inodekey(m), adr1], asynced0 → boolvar1 ⊦ ∃ err0. ⌊err0⌋ ∧ ⟨err := err0; asynced0 := ?⟩ ( abs-dirs(fs0, ri) = abs-dirs(fs0[adr1, inodenode(inodekey(m), md, false, m0, 0, m2)], ri[inodekey(m), adr1]) ∧ abs-files(fs0, ri) = abs-files(fs0[adr1, inodenode(inodekey(m), md, false, m0, 0, m2)], ri[inodekey(m), adr1]) ∧ orphans(fs0[adr1, inodenode(inodekey(m), md, false, m0, 0, m2)], ri[inodekey(m), adr1]) = orphans(fs0, ri) ∧ (asynced0 → boolvar) ∧ ESUCCESS = err), abs-dir(ino, fs0[adr1, inodenode(inodekey(m), md, false, m0, 0, m2)], ri[inodekey(m), adr1]) = mkdir (fs0[ri[inodekey(ino)]].size, fs0[ri[inodekey(ino)]].meta, fs0[ri[inodekey(ino)]].nlink, fs0[ri[inodekey(ino)]].nsubdirs, abs-children(ino, fs0, ri)), adr1 = ri[inodekey(ino)], ino = m, m = 0, adr1 ∈ fs0

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] → [ino, ri[inodekey(m), adr1], fs0[adr1, inodenode(inodekey(m), md, false, m0, 0, m2)]] flags: <all paths>

Additional information

Used simplifier rules: at-ri: ⊦ ri[key, adr][key0] = (key = key0 ⊃ adr;ri[key0]);% ⊦ inodekey(m) = inodekey(m0) ↔ m = m0; (s)% ⊦ adr ≠ adr0 → fs[adr0, nd][adr] = fs[adr]; (s)% ⊦ key ∈ ri[key0, adr] ↔ key = key0 ∨ key ∈ ri; (ws) Used terms: ino, ri[inodekey(m), adr1], fs0[adr1, inodenode(inodekey(m), md, false, m0, 0, m2)]