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Proof step 31 from proof inv-readpage (previous step)

# buf = VFS_PAGE_SIZE, files[m].content[pageno] ≠ zeropage, 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, pageno ∈ files[m].content, ¬ datakey(m, pageno) ∈ pcache, asynced2 → synced(files, icache, pcache) ⊦ ⟪let asynced = false in {err := ESUCCESS; pcache_set#(m, pageno, files[m].content[pageno], asynced; err, pcache)}⟫ (pcache-cons(pcache, dirs, files) ∧ synced(dirs, icache, pcache) ∧ (asynced2 → synced(files, icache, pcache)))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 32:
# buf = VFS_PAGE_SIZE, files[m] = mkfile(m0, md, m1, content), afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), pageno ∈ content, m ∈ files, asynced2 → synced(files, icache, pcache) ⊦ ⟪let asynced = false in {err := ESUCCESS; pcache_set#(m, pageno, content[pageno], asynced; err, pcache)}⟫ (pcache-cons(pcache, dirs, files) ∧ synced(dirs, icache, pcache) ∧ (asynced2 → synced(files, icache, pcache))), content[pageno] = zeropage, datakey(m, pageno) ∈ 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