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Proof step 3 from proof pcache-overwrite-read-page (previous step)

files[ino] = mkfile(m, md, m0, content), n ∈ content, ino ∈ files ⊦ files ⊕ pcache[datakey(ino, n), mkpentry(false, content[n])] = files ⊕ pcache, datakey(ino, n) ∈ pcache

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ files = files0 ↔ (∀ ino. (ino ∈ files ↔ ino ∈ files0) ∧ (ino ∈ files → files[ino] = files0[ino]))
Proof step 5:
files[ino] = mkfile(m, md, m0, content), ino ∈ files, n ∈ content ⊦ datakey(ino, n) ∈ pcache, ∀ ino0. (ino0 ∈ files ⊕ pcache[datakey(ino, n), mkpentry(false, content[n])] ↔ ino0 ∈ files ⊕ pcache) ∧ ( ino0 ∈ files ⊕ pcache[datakey(ino, n), mkpentry(false, content[n])] → (files ⊕ pcache[datakey(ino, n), mkpentry(false, content[n])])[ino0] = (files ⊕ pcache)[ino0])

Rule argument

spec: heap, inst: file-heap name: ext seq: ⊦ files = files0 ↔ (∀ ino. (ino ∈ files ↔ ino ∈ files0) ∧ (ino ∈ files → files[ino] = files0[ino])) subst: [files0, files] → [files ⊕ pcache, files ⊕ pcache[datakey(ino, n), mkpentry(false, content[n])]] flags: <all paths>

Additional information

Used terms: files ⊕ pcache, files ⊕ pcache[datakey(ino, n), mkpentry(false, content[n])]