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Proof step 150 from proof refine-write-inode (previous step)

fs0[ri[inodekey(m)]] = inodenode(key, md0, false, m0, 0, m3), key0.ino ≠ ROOT_INO, ¬ ( key0 ∈ ri ∧ fs0[ri[key0]].nlink = 0 ↔ key0 ∈ ri[inodekey(m), adr1] ∧ (adr1 = (inodekey(m) = key0 ⊃ adr1;ri[key0]) ⊃ inodenode(inodekey(m), md, false, m0, 0, m2);fs0[(inodekey(m) = key0 ⊃ adr1;ri[key0])]).nlink = 0), m ≠ 0, key0.inode?, 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(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]) ∧ (∀ 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, false, m0, 0, m2) ;fs0[(inodekey(m) = key1 ⊃ adr1;ri[key1])] ) .nlink = 0)) ∧ (asynced0 → boolvar) ∧ ESUCCESS = err)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 151:
fs0[ri[inodekey(m)]] = inodenode(key, md0, false, m0, 0, m3), key0 = inodekey(m1), key0.inode?, 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, 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]) ∧ (∀ 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, false, m0, 0, m2) ;fs0[(inodekey(m) = key1 ⊃ adr1;ri[key1])] ) .nlink = 0)) ∧ (asynced0 → boolvar) ∧ ESUCCESS = err), key0 ∈ ri ∧ fs0[ri[key0]].nlink = 0 ↔ key0 ∈ ri[inodekey(m), adr1] ∧ (adr1 = (inodekey(m) = key0 ⊃ adr1;ri[key0]) ⊃ inodenode(inodekey(m), md, false, m0, 0, m2);fs0[(inodekey(m) = key0 ⊃ adr1;ri[key0])]).nlink = 0, m = 0, m1 = ROOT_INO, adr1 ∈ fs0

Rule argument

spec: key name: elim-01 seq: ⊦ key.inode? → (m = key.ino ↔ key = inodekey(m)) subst: [key, m] → [key0, m1]

Additional information

Used simplifier rules: ⊦ key.inode? → (m = key.ino ↔ key = inodekey(m)); (elim) Used terms: key0, m1