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Proof step 78 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), pageno ∈ content, m ∈ files, asynced2 → synced(files, icache, pcache) ⊦ content[pageno] = zeropage, datakey(m, pageno) ∈ pcache, ∀ key. key ∈ pcache[datakey(m, pageno), mkpentry(false, content[pageno])] → key.data? ∧ # pcache[datakey(m, pageno), mkpentry(false, content[pageno])][key].page = VFS_PAGE_SIZE ∧ valid-file-ino(key.ino, dirs, 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 simplifier applied rule simplifier

And obtained the following new goals

Proof step 79:
# 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])

Rule argument

Additional information

Used simplifier rules: ⊦ valid-file-ino(ino, dirs, files) ↔ ino ∈ files; (s)