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Proof step 94 from proof refine-write-inode (previous step)

fs0[ri[inodekey(m)]] = inodenode(key, md0, true, m0, m1, m3), ¬ ( inodekey(m2) ∈ ri ∧ fs0[ri[inodekey(m2)]].nlink = 0 ↔ inodekey(m2) ∈ ri[inodekey(m), adr1] ∧ (adr1 = ri[inodekey(m2)] ⊃ inodenode(inodekey(m), md, true, m0, m1, m3);fs0[ri[inodekey(m2)]]).nlink = 0), m ≠ 0, m2 ≠ ROOT_INO, m2 ≠ m, 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]) ∧ (∀ key1. key1.inode? ∧ key1.ino ≠ ROOT_INO → ( key1 ∈ ri ∧ fs0[ri[key1]].nlink = 0 ↔ key1 ∈ ri[inodekey(m), adr1] ∧ (adr1 = (inodekey(m) = key1 ⊃ adr1;ri[key1]) ⊃ inodenode(inodekey(m), md, true, m0, m1, m3) ;fs0[(inodekey(m) = key1 ⊃ adr1;ri[key1])] ) .nlink = 0)) ∧ (asynced0 → boolvar) ∧ ESUCCESS = err)

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 95:
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, inodekey(m2) ∈ ri, 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]) ∧ (∀ key1. key1.inode? ∧ key1.ino ≠ ROOT_INO → ( key1 ∈ ri ∧ fs0[ri[key1]].nlink = 0 ↔ key1 ∈ ri[inodekey(m), adr1] ∧ (adr1 = (inodekey(m) = key1 ⊃ adr1;ri[key1]) ⊃ inodenode(inodekey(m), md, true, m0, m1, m3) ;fs0[(inodekey(m) = key1 ⊃ adr1;ri[key1])] ) .nlink = 0)) ∧ (asynced0 → boolvar) ∧ ESUCCESS = err), inodekey(m2) ∈ ri ∧ fs0[ri[inodekey(m2)]].nlink = 0 ↔ inodekey(m2) ∈ ri[inodekey(m), adr1] ∧ (adr1 = ri[inodekey(m2)] ⊃ inodenode(inodekey(m), md, true, m0, m1, m3);fs0[ri[inodekey(m2)]]).nlink = 0, m = 0, m2 = ROOT_INO, m2 = m, adr1 ∈ fs0

Rule argument

fma: inodekey(m2) ∈ ri

Additional information

Used simplifier rules: ⊦ key ∈ ri[key0, adr] ↔ key = key0 ∨ key ∈ ri; (ws)% ⊦ inodekey(m) = inodekey(m0) ↔ m = m0; (s) Used formulas: inodekey(m2) ∈ ri