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Proof step 5 from proof fsync-pages-inv (previous step)

m0 = files[m].nlink, afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), m ∈ files ⊦ ⟪cache_fsync-pages#(mkinode(m, md, false, files[m].nlink, 0, m2), dirs; err, files, pcache, asynced)⟫ ( icache-cons(icache, dirs, files) ∧ dcache-cons(dcache, dirs, files) ∧ pcache-cons(pcache, dirs, files) ∧ afs-cons(dirs, files) ∧ synced(dirs, icache, pcache) ∧ m ∈ files ∧ m0 = files[m].nlink)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 6:
files[m] = mkfile(m1, md0, m3, content), m0 = m3, afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), m ∈ files ⊦ ⟪cache_fsync-pages#(mkinode(m, md, false, m3, 0, m2), dirs; err, files, pcache, asynced)⟫ ( icache-cons(icache, dirs, files) ∧ dcache-cons(dcache, dirs, files) ∧ pcache-cons(pcache, dirs, files) ∧ afs-cons(dirs, files) ∧ synced(dirs, icache, pcache) ∧ m ∈ files ∧ m0 = files[m].nlink)

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] → [files[m], m0, md0, m1, content]

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: files[m], m0, md0, m1, content