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Proof step 372 from proof inv-write_inode (previous step)

afs-cons(dirs, files), afs-cons(dirs, files[m, (files[m].meta:= md).size:= m2]), pcache-cons(pcache, dirs, files), synced(files, icache, pcache), synced(dirs, icache, pcache), key ∈ pcache, m ∈ files ⊦ m ∈ icache, key.data? ∧ # pcache[key].page = VFS_PAGE_SIZE ∧ key.ino ∈ files ∧ ( ¬ pcache[key].dirty → key.part ∈ (key.ino = m ⊃ (files[key.ino].meta:= md).size:= m2;files[key.ino]).content ∧ pcache[key].page = (key.ino = m ⊃ (files[key.ino].meta:= md).size:= m2;files[key.ino]).content[key.part])

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 373:
pcache[key] = mkpentry(boolvar, buf), afs-cons(dirs, files[m, (files[m].meta:= md).size:= m2]), afs-cons(dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), synced(files, icache, pcache), m ∈ files, key ∈ pcache ⊦ m ∈ icache, key.data? ∧ # buf = VFS_PAGE_SIZE ∧ key.ino ∈ files ∧ ( ¬ boolvar → key.part ∈ (key.ino = m ⊃ (files[key.ino].meta:= md).size:= m2;files[key.ino]).content ∧ buf = (key.ino = m ⊃ (files[key.ino].meta:= md).size:= m2;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[key], boolvar, buf]

Additional information

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