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Proof step 106 from proof refine-evict (previous step)

fs[ri[inodekey(m0)]].nlink = 0, fs[ri[inodekey(m0)]].nsubdirs = # subdirs(m0, abs-dirs(fs, ri)), fs[ri[inodekey(m0)]].size = 0, abs-children(m0, fs, ri) = ∅, links(m0, abs-dirs(fs, ri)) = ∅, fs[ri[inodekey(ROOT_INO)]].directory, orphans(fs, ri).inodes?, fo.inodes?, file-node-cons(fs, ri), log-cons(log, fs), orphans-cons(fs, ri, orphans(fs, ri)), 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), inodekey(m) ∈ ri, dentrykey(m0, str) ∈ ri, inodekey(m0) ∈ ri, inodekey(ROOT_INO) ∈ ri, asynced → boolvar, ∀ name. dentrykey(m0, name) ∈ ri → inodekey(abs-dirs(fs, ri)[m0].entries[name]) ∈ ri ∧ fs[ri[inodekey(abs-dirs(fs, ri)[m0].entries[name])]].directory ∨ inodekey(abs-dirs(fs, ri)[m0].entries[name]) ∈ ri ∧ ¬ fs[ri[inodekey(abs-dirs(fs, ri)[m0].entries[name])]].directory, fs[ri[inodekey(m)]].directory ∧ m2 = fs[ri[inodekey(m)]].size ∧ m1 = fs[ri[inodekey(m)]].nsubdirs ∧ boolvar0 ∨ ¬ fs[ri[inodekey(m)]].directory ∧ m1 = 0 ∧ ¬ boolvar0 ⊦ # dentrykeys(inodekey(m0), ri) = 0, dentrykeys(inodekey(m0), ri) = ∅, m = ROOT_INO, m0 = ROOT_INO

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 107:
fs[ri[inodekey(m0)]].nlink = 0, fs[ri[inodekey(m0)]].nsubdirs = # subdirs(m0, abs-dirs(fs, ri)), fs[ri[inodekey(m0)]].size = 0, abs-dirs(fs, ri)[m0] = mkdir(m3, md, m4, m5, entries), abs-children(m0, fs, ri) = ∅, links(m0, abs-dirs(fs, ri)) = ∅, fs[ri[inodekey(ROOT_INO)]].directory, fo.inodes?, orphans(fs, ri).inodes?, file-node-cons(fs, ri), log-cons(log, fs), orphans-cons(fs, ri, orphans(fs, ri)), 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), inodekey(ROOT_INO) ∈ ri, inodekey(m0) ∈ ri, dentrykey(m0, str) ∈ ri, inodekey(m) ∈ ri, asynced → boolvar, ∀ name. dentrykey(m0, name) ∈ ri → inodekey(entries[name]) ∈ ri ∧ fs[ri[inodekey(entries[name])]].directory ∨ inodekey(entries[name]) ∈ ri ∧ ¬ fs[ri[inodekey(entries[name])]].directory, fs[ri[inodekey(m)]].directory ∧ m2 = fs[ri[inodekey(m)]].size ∧ m1 = fs[ri[inodekey(m)]].nsubdirs ∧ boolvar0 ∨ ¬ fs[ri[inodekey(m)]].directory ∧ m1 = 0 ∧ ¬ boolvar0 ⊦ # dentrykeys(inodekey(m0), ri) = 0, dentrykeys(inodekey(m0), ri) = ∅, m = ROOT_INO, m0 = ROOT_INO

Rule argument

spec: abstract-dir name: elim seq: ⊦ ( ((m = ad.size ∧ md = ad.meta) ∧ m0 = ad.nlink) ∧ m1 = ad.nsubdirs) ∧ entries = ad.entries ↔ ad = mkdir(m, md, m0, m1, entries) subst: [ad, m, md, m0, m1, entries] → [abs-dirs(fs, ri)[m0], m3, md, m4, m5, entries]

Additional information

Used simplifier rules: ⊦ ( ((m = ad.size ∧ md = ad.meta) ∧ m0 = ad.nlink) ∧ m1 = ad.nsubdirs) ∧ entries = ad.entries ↔ ad = mkdir(m, md, m0, m1, entries); (elim) Used terms: abs-dirs(fs, ri)[m0], m3, md, m4, m5, entries