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Proof step 77 from proof crash-neutral-rmdir (previous step)

(entries0[str] = m ⊃ mkdir(m1, md3, # links(entries0[str], dirs0), m4 - 1, entries0 -- str) ;mkdir(m3, md1, # links(entries0[str], dirs0), m2, ∅) ) .nlink = 0, dirs0[entries0[str]] = mkdir(m3, md1, # links(entries0[str], dirs0), m2, ∅), dirs0[m] = mkdir(m1 + 1, md3, # links(m, dirs0), m4, entries0), # links(m, dirs0) ≠ 0, entries0[str] ≠ ROOT_INO, links(m, dirs0) ≠ ∅, m ≠ ROOT_INO, m4 ≠ 0, afs-cons(dirs0, files), m ∈ dirs0, entries0[str] ∈ dirs0, str ∈ entries0, 1 ≤ m4 ⊦ ⟨fail#(; ; err); asynced := ?⟩ asynced

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 78:
(entries0[str] = m ⊃ mkdir(m1, md3, # links(entries0[str], dirs0), m4 - 1, entries0 -- str) ;mkdir(m3, md1, # links(entries0[str], dirs0), m2, ∅) ) = mkdir(m0, md, m5, m6, entries), dirs0[m] = mkdir(m1 + 1, md3, # links(m, dirs0), m4, entries0), dirs0[entries0[str]] = mkdir(m3, md1, # links(entries0[str], dirs0), m2, ∅), m5 = 0, afs-cons(dirs0, files), str ∈ entries0, entries0[str] ∈ dirs0, m ∈ dirs0, 1 ≤ m4 ⊦ ⟨fail#(; ; err); asynced := ?⟩ asynced, # links(m, dirs0) = 0, entries0[str] = ROOT_INO, links(m, dirs0) = ∅, m = ROOT_INO, m4 = 0

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] → [(entries0[str] = m ⊃ mkdir (m1, md3, # links(entries0[str], dirs0), m4 - 1, entries0 -- str) ;mkdir(m3, md1, # links(entries0[str], dirs0), m2, ∅) ), m0, md, m5, m6, 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: (entries0[str] = m ⊃ mkdir (m1, md3, # links(entries0[str], dirs0), m4 - 1, entries0 -- str) ;mkdir(m3, md1, # links(entries0[str], dirs0), m2, ∅) ), m0, md, m5, m6, entries