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Proof step 58 from proof rename-precond-abs (previous step)

key.ino = fs[ri[dentrykey(m3, str0)]].ino, key.dentry?, fs[ri[inodekey(m4)]].directory, fs[ri[inodekey(m3)]].directory, fs[ri[inodekey(key.ino)]].directory, fs[ri[inodekey(fs[ri[dentrykey(m4, str)]].ino)]].directory, orphans(fs, ri).inodes?, afs-cons(abs-dirs(fs, ri), abs-files(fs, ri)), file-node-cons(fs, ri), log-cons(log, fs), replay-cons-strong(fs, ri, orphans(fs, ri), fi, fo, log), ri-inj(fi), ri-inj(ri), ubifs-cons(fs, ri, orphans(fs, ri), fi, fo, log), key ∈ ri, inodekey(key.ino) ∈ ri, inodekey(fs[ri[dentrykey(m4, str)]].ino) ∈ ri, dentrykey(m4, str) ∈ ri, inodekey(m3) ∈ ri, inodekey(m4) ∈ ri, dentrykey(m3, str0) ∈ ri, m3 = m4 → md = md0, ∀ str1. ¬ dentrykey(key.ino, str1) ∈ ri ∧ abs-children(key.ino, fs, ri)[str1] = (∅)[str1], links(m4, abs-dirs(fs, ri)) ≠ ∅ ∨ m4 = ROOT_INO, links(m3, abs-dirs(fs, ri)) ≠ ∅ ∨ m3 = ROOT_INO ⊦ # dentrykeys(inodekey(key.ino), ri) = 0, key.ino = ROOT_INO, dentrykeys(inodekey(key.ino), ri) = ∅

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 59:
key = dentrykey(m, str2), m = fs[ri[dentrykey(m3, str0)]].ino, key.dentry?, fs[ri[inodekey(fs[ri[dentrykey(m4, str)]].ino)]].directory, fs[ri[inodekey(m)]].directory, fs[ri[inodekey(m3)]].directory, fs[ri[inodekey(m4)]].directory, orphans(fs, ri).inodes?, afs-cons(abs-dirs(fs, ri), abs-files(fs, ri)), file-node-cons(fs, ri), log-cons(log, fs), replay-cons-strong(fs, ri, orphans(fs, ri), fi, fo, log), ri-inj(ri), ri-inj(fi), ubifs-cons(fs, ri, orphans(fs, ri), fi, fo, log), dentrykey(m3, str0) ∈ ri, inodekey(m4) ∈ ri, inodekey(m3) ∈ ri, dentrykey(m4, str) ∈ ri, inodekey(fs[ri[dentrykey(m4, str)]].ino) ∈ ri, inodekey(m) ∈ ri, key ∈ ri, m3 = m4 → md = md0, ∀ str1. ¬ dentrykey(m, str1) ∈ ri ∧ abs-children(m, fs, ri)[str1] = (∅)[str1], links(m3, abs-dirs(fs, ri)) ≠ ∅ ∨ m3 = ROOT_INO, links(m4, abs-dirs(fs, ri)) ≠ ∅ ∨ m4 = ROOT_INO ⊦ # dentrykeys(inodekey(m), ri) = 0, dentrykeys(inodekey(m), ri) = ∅, m = ROOT_INO

Rule argument

spec: key name: elim-03 seq: ⊦ key.dentry? → (m = key.ino ∧ str = key.name ↔ key = dentrykey(m, str)) subst: [key, m, str] → [key, m, str2]

Additional information

Used simplifier rules: ⊦ key.dentry? → (m = key.ino ∧ str = key.name ↔ key = dentrykey(m, str)); (elim) Used terms: key, m, str2