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Proof step 55 from proof refine-write-inode (previous step)

fs0[ri[inodekey(m)]] = inodenode(key, md0, true, m0, m1, m3), m ≠ 0, fo.inodes?, orphans(fs0, ri).inodes?, afs-cons(abs-dirs(fs0, ri)[m, abs-dirs(fs0, ri)[m].meta:= md], abs-files(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, ¬ adr1 ∈ fs0, asynced0 → boolvar1 ⊦ ∃ err0. ⌊err0⌋ ∧ ⟨err := err0; asynced0 := ?⟩ ( abs-dirs(fs0, ri) = abs-dirs(fs0[adr1, inodenode(inodekey(m), md, true, m0, m1, m3)], ri[inodekey(m), adr1]) ∧ abs-files(fs0, ri) = abs-files(fs0[adr1, inodenode(inodekey(m), md, true, m0, m1, m3)], ri[inodekey(m), adr1]) ∧ orphans(fs0[adr1, inodenode(inodekey(m), md, true, m0, m1, m3)], ri[inodekey(m), adr1]) = orphans(fs0, ri) ∧ (asynced0 → boolvar) ∧ ESUCCESS = err), (dentrykey(m, str) ∈ ri → dentrykey(m, str) ∈ ri[inodekey(m), adr1]) ∧ ( dentrykey(m, str) ∈ ri[inodekey(m), adr1] → (adr1 = ri[dentrykey(m, str)] ⊃ inodenode(inodekey(m), md, true, m0, m1, m3);fs0[ri[dentrykey(m, str)]]).ino = fs0[ri[dentrykey(m, str)]].ino)

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 56:
fs0[ri[inodekey(m)]] = inodenode(key, md0, true, m0, m1, m3), orphans(fs0, ri).inodes?, fo.inodes?, afs-cons(abs-dirs(fs0, ri), abs-files(fs0, ri)), afs-cons(abs-dirs(fs0, ri)[m, abs-dirs(fs0, ri)[m].meta:= md], 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(ri), ri-inj(fi), ubifs-cons(fs0, ri, orphans(fs0, ri), fi, fo, log0), inodekey(m) ∈ ri, ri[inodekey(m)] ∈ fs0, asynced0 → boolvar1 ⊦ ∃ err0. ⌊err0⌋ ∧ ⟨err := err0; asynced0 := ?⟩ ( abs-dirs(fs0, ri) = abs-dirs(fs0[adr1, inodenode(inodekey(m), md, true, m0, m1, m3)], ri[inodekey(m), adr1]) ∧ abs-files(fs0, ri) = abs-files(fs0[adr1, inodenode(inodekey(m), md, true, m0, m1, m3)], ri[inodekey(m), adr1]) ∧ orphans(fs0[adr1, inodenode(inodekey(m), md, true, m0, m1, m3)], ri[inodekey(m), adr1]) = orphans(fs0, ri) ∧ (asynced0 → boolvar) ∧ ESUCCESS = err), dentrykey(m, str) = inodekey(m), m = 0, adr1 ∈ fs0, (dentrykey(m, str) ∈ ri → dentrykey(m, str) ∈ ri[inodekey(m), adr1]) ∧ ( dentrykey(m, str) ∈ ri[inodekey(m), adr1] → (adr1 = ri[dentrykey(m, str)] ⊃ inodenode(inodekey(m), md, true, m0, m1, m3);fs0[ri[dentrykey(m, str)]]).ino = fs0[ri[dentrykey(m, str)]].ino)

Rule argument

fma: dentrykey(m, str) = inodekey(m)

Additional information

Used simplifier rules: ⊦ inodekey(m) ≠ dentrykey(m0, str); (s) Used formulas: dentrykey(m, str) = inodekey(m)