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Proof step 87 from proof inv-fsync (previous step)

# links(m, dirs) = files0[m].nlink, files1[m] = mkfile(m1, md1, files0[m].nlink, content0), files0[m] = mkfile(m0, md0, files0[m].nlink, content), afs-cons(dirs, files1), afs-cons(dirs, files0), dcache-cons(dcache, dirs, files1), dcache-cons(dcache, dirs, files0), icache-cons(icache, dirs, files1), icache-cons(icache, dirs, files0), pcache-cons(pcache, dirs, files1), pcache-cons(pcache0, dirs, files0), synced(dirs, icache, pcache), synced(dirs, icache, pcache0), m ∈ files1, m ∈ files0 ⊦ ⟪fail_or_success#(; ; err); choose bv with true in asynced := bv⟫ true

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 88:
# links(m, dirs) = m3, files0[m] = mkfile(m0, md0, m3, content), files1[m] = mkfile(m1, md1, m3, content0), files0[m] = mkfile(m2, md, m3, content1), afs-cons(dirs, files0), afs-cons(dirs, files1), dcache-cons(dcache, dirs, files0), dcache-cons(dcache, dirs, files1), icache-cons(icache, dirs, files0), icache-cons(icache, dirs, files1), pcache-cons(pcache0, dirs, files0), pcache-cons(pcache, dirs, files1), synced(dirs, icache, pcache0), synced(dirs, icache, pcache), m ∈ files0, m ∈ files1 ⊦ ⟪fail_or_success#(; ; err); choose bv with true in asynced := bv⟫ true

Rule argument

spec: abstract-file name: elim seq: ⊦ ((m = af.size ∧ md = af.meta) ∧ m0 = af.nlink) ∧ content = af.content ↔ af = mkfile(m, md, m0, content) subst: [af, m, md, m0, content] → [files0[m], m2, md, m3, content1]

Additional information

Used simplifier rules: ⊦ ((m = af.size ∧ md = af.meta) ∧ m0 = af.nlink) ∧ content = af.content ↔ af = mkfile(m, md, m0, content); (elim) Used terms: files0[m], m2, md, m3, content1