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Proof step 22 from proof inv-fsync (previous step)

# links(m, dirs) = files0[m].nlink, files[m] = mkfile(m1, md1, files0[m].nlink, content0), err0 = ESUCCESS, inode = mkinode(m, md, false, files0[m].nlink, 0, m2), afs-cons(dirs, files), afs-cons(dirs, files0), dcache-cons(dcache, dirs, files), dcache-cons(dcache, dirs, files0), icache-cons(icache, dirs, files), icache-cons(icache, dirs, files0), pcache-cons(pcache, dirs, files), pcache-cons(pcache0, dirs, files0), synced(dirs, icache, pcache), synced(dirs, icache, pcache0), m ∈ files, m ∈ files0 ⊦ ⟪cache_fsync-inode#(; inode, err0, dirs, files0, icache, asynced); if err0 = ESUCCESS then afs_fsync#(inode, false, dirs, files0; ; asynced, err0)⟫ ( icache-cons(icache, dirs, files0) ∧ dcache-cons(dcache, dirs, files0) ∧ pcache-cons(pcache0, dirs, files0) ∧ synced(dirs, icache, pcache0) ∧ afs-cons(dirs, files0))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 23:
# links(m, dirs) = m3, files[m] = mkfile(m1, md1, m3, content0), files0[m] = mkfile(m0, md0, m3, content), err0 = ESUCCESS, inode = mkinode(m, md, false, m3, 0, m2), afs-cons(dirs, files0), afs-cons(dirs, files), dcache-cons(dcache, dirs, files0), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files0), icache-cons(icache, dirs, files), pcache-cons(pcache0, dirs, files0), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache0), synced(dirs, icache, pcache), m ∈ files0, m ∈ files ⊦ ⟪cache_fsync-inode#(; inode, err0, dirs, files0, icache, asynced); if err0 = ESUCCESS then afs_fsync#(inode, false, dirs, files0; ; asynced, err0)⟫ ( icache-cons(icache, dirs, files0) ∧ dcache-cons(dcache, dirs, files0) ∧ pcache-cons(pcache0, dirs, files0) ∧ synced(dirs, icache, pcache0) ∧ afs-cons(dirs, files0))

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], m0, md0, m3, 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: files0[m], m0, md0, m3, content