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Proof step 40 from proof inv-fsync (previous step)

# links(m0, dirs0) = files1[m0].nlink, files1[m0] = mkfile(m2, md0, files1[m0].nlink, content), files0[m] = mkfile(m3, md2, # links(m, dirs1), content1), files2[m] = mkfile(m1, md1, # links(m, dirs1), content0), afs-cons(dirs0, files1), afs-cons(dirs1, files0), afs-cons(dirs1, files2), dcache-cons(dcache, dirs0, files1), dcache-cons(dcache, dirs1, files0), dcache-cons(dcache, dirs1, files2), icache-cons(icache0, dirs0, files1), icache-cons(icache, dirs1, files0), icache-cons(icache, dirs1, files2), pcache-cons(pcache0, dirs0, files1), pcache-cons(pcache0, dirs1, files0), pcache-cons(pcache, dirs1, files2), synced(dirs0, icache0, pcache0), synced(dirs1, icache, pcache0), synced(dirs1, icache, pcache), m0 ∈ files1, m ∈ files2, 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 41:
# links(m0, dirs0) = m5, files2[m] = mkfile(m1, md1, # links(m, dirs1), content0), files0[m] = mkfile(m3, md2, # links(m, dirs1), content1), files1[m0] = mkfile(m2, md0, m5, content), files1[m0] = mkfile(m4, md, m5, content2), afs-cons(dirs1, files2), afs-cons(dirs1, files0), afs-cons(dirs0, files1), dcache-cons(dcache, dirs1, files2), dcache-cons(dcache, dirs1, files0), dcache-cons(dcache, dirs0, files1), icache-cons(icache, dirs1, files2), icache-cons(icache, dirs1, files0), icache-cons(icache0, dirs0, files1), pcache-cons(pcache, dirs1, files2), pcache-cons(pcache0, dirs1, files0), pcache-cons(pcache0, dirs0, files1), synced(dirs1, icache, pcache), synced(dirs1, icache, pcache0), synced(dirs0, icache0, pcache0), m ∈ files0, m ∈ files2, m0 ∈ 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] → [files1[m0], m4, md, m5, content2]

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: files1[m0], m4, md, m5, content2