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Proof step 179 from proof fsync-inode-inv (previous step)

icache[m] = mkientry(false, inode), files[m] = mkfile(m0, md0, # links(m, dirs), content), err = ESUCCESS, afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), m ∈ icache, m ∈ files ⊦ ⟪icache_set_status#(m, false; err, icache)⟫ (icache-cons(icache, dirs, files) ∧ synced(dirs, icache, pcache) ∧ # links(m, dirs) = files[m].nlink)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 180:
files[m] = mkfile(m0, md0, # links(m, dirs), content), icache[m] = mkientry(false, inode), files[m] = mkfile(m1, md, m2, content0), err = ESUCCESS, 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, m ∈ icache ⊦ ⟪icache_set_status#(m, false; err, icache)⟫ (icache-cons(icache, dirs, files) ∧ synced(dirs, icache, pcache) ∧ # links(m, dirs) = m2)

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], m1, md, m2, content0]

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], m1, md, m2, content0