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Proof step 17 from proof pcache-overwrite-read-page (previous step)

files[ino0] = mkfile(m1, md0, m2, content0), files[ino] = mkfile(m, md, m0, content), n ∈ content, ino ∈ files, ino0 ∈ files ⊦ n0 ∈ content0 ∨ datakey(ino0, n0) ∈ pcache[datakey(ino, n), mkpentry(false, content[n])] ↔ n0 ∈ content0 ⊕ mkcontent(ino0, pcache), datakey(ino, n) ∈ pcache

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 18:
⊦ key ∈ pcache[key0, pe] ↔ key = key0 ∨ key ∈ pcache

Rule argument

spec: store, inst: pcache-wb name: In-insert seq: ⊦ key ∈ pcache[key0, pe] ↔ key = key0 ∨ key ∈ pcache subst: [pe, key0, pcache, key] → [mkpentry(false, content[n]), datakey(ino, n), pcache, datakey(ino0, n0)] flags: <all paths>

Additional information

Used simplifier rules: in-overwrite-content: ⊦ n ∈ content0 ⊕ content1 ↔ n ∈ content0 ∨ n ∈ content1;%in-mkcontent: ⊦ n ∈ mkcontent(ino, pcache) ↔ datakey(ino, n) ∈ pcache;%in-overwrite-content: ⊦ n ∈ content0 ⊕ content1 ↔ n ∈ content0 ∨ n ∈ content1;% ⊦ datakey(m, m0) = datakey(m1, m2) ↔ m = m1 ∧ m0 = m2; (ws)%⊦ mkfile(m, md, m0, content) = mkfile(m1, md0, m2, content0) ↔ m = m1 ∧ md = md0 ∧ m0 = m2 ∧ content = content0; (ws) Used terms: mkpentry(false, content[n]), datakey(ino, n), pcache, datakey(ino0, n0)