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Proof step 79 from proof inv-readpage (previous step)

# buf0 = VFS_PAGE_SIZE, files[m] = mkfile(m0, md, # links(m, dirs), content), afs-cons(dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), key ∈ pcache[datakey(m, pageno), mkpentry(false, content[pageno])], m ∈ files, pageno ∈ content, asynced2 → synced(files, icache, pcache) ⊦ content[pageno] = zeropage, datakey(m, pageno) ∈ pcache, key.data? ∧ # pcache[datakey(m, pageno), mkpentry(false, content[pageno])][key].page = VFS_PAGE_SIZE ∧ key.ino ∈ files ∧ ( ¬ pcache[datakey(m, pageno), mkpentry(false, content[pageno])][key].dirty → key.part ∈ files[key.ino].content ∧ pcache[datakey(m, pageno), mkpentry(false, content[pageno])][key].page = files[key.ino].content[key.part])

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 80:
# buf0 = VFS_PAGE_SIZE, files[m] = mkfile(m0, md, # links(m, dirs), content), pcache[datakey(m, pageno), mkpentry(false, content[pageno])][key] = mkpentry(boolvar, buf), afs-cons(dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), pageno ∈ content, m ∈ files, key ∈ pcache[datakey(m, pageno), mkpentry(false, content[pageno])], asynced2 → synced(files, icache, pcache) ⊦ content[pageno] = zeropage, datakey(m, pageno) ∈ pcache, key.data? ∧ # buf = VFS_PAGE_SIZE ∧ key.ino ∈ files ∧ (¬ boolvar → key.part ∈ files[key.ino].content ∧ buf = files[key.ino].content[key.part])

Rule argument

spec: pcache-entry name: elim seq: ⊦ (boolvar ↔ pe.dirty) ∧ buf = pe.page ↔ pe = mkpentry(boolvar, buf) subst: [pe, boolvar, buf] → [pcache[datakey(m, pageno), mkpentry(false, content[pageno])] [key ], boolvar, buf]

Additional information

Used simplifier rules: ⊦ (boolvar ↔ pe.dirty) ∧ buf = pe.page ↔ pe = mkpentry(boolvar, buf); (elim) Used terms: pcache[datakey(m, pageno), mkpentry(false, content[pageno])][key], boolvar, buf