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

# buf = VFS_PAGE_SIZE, err = ESUCCESS, afs-cons(dirs, files), afs-cons(dirs, files[m, files[m].content:= files[m].content[pageno, buf]]), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(files, icache, pcache), synced(dirs, icache, pcache), m ∈ files ⊦ ⟪asynced2 := false; if err = ESUCCESS then pcache_set#(m, pageno, buf, asynced2; err, pcache)⟫ ( icache-cons(icache, dirs, files[m, files[m].content:= files[m].content[pageno, buf]]) ∧ dcache-cons(dcache, dirs, files[m, files[m].content:= files[m].content[pageno, buf]]) ∧ pcache-cons(pcache, dirs, files[m, files[m].content:= files[m].content[pageno, buf]]) ∧ synced(dirs, icache, pcache) ∧ synced(files[m, files[m].content:= files[m].content[pageno, buf]], icache, pcache))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 23:
# buf = VFS_PAGE_SIZE, files[m] = mkfile(m0, md, m1, content), err = ESUCCESS, afs-cons(dirs, files[m, files[m].content:= content[pageno, buf]]), afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), synced(files, icache, pcache), m ∈ files ⊦ ⟪asynced2 := false; if err = ESUCCESS then pcache_set#(m, pageno, buf, asynced2; err, pcache)⟫ ( icache-cons(icache, dirs, files[m, files[m].content:= content[pageno, buf]]) ∧ dcache-cons(dcache, dirs, files[m, files[m].content:= content[pageno, buf]]) ∧ pcache-cons(pcache, dirs, files[m, files[m].content:= content[pageno, buf]]) ∧ synced(dirs, icache, pcache) ∧ synced(files[m, files[m].content:= content[pageno, buf]], icache, pcache))

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, md, 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, md, m1, content