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Proof step 154 from proof overwrite-write-page-dirty (previous step)

files[ino0] = mkfile(m4, md0, m5, content), icache[ino0] = mkientry(boolvar, mkinode(m0, md, true, m1, m2, m3)), ino0 ∈ icache, ino ∈ files, ino0 ∈ files ⊦ n ∈ content ⊕ mkcontent(ino0, pcache) ↔ n ∈ content ∨ datakey(ino0, n) ∈ pcache[datakey(ino, m), mkpentry(true, buf)], ino ∈ icache

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 155:
⊦ 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(true, buf), datakey(ino, m), pcache, datakey(ino0, n)] 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) Used terms: mkpentry(true, buf), datakey(ino, m), pcache, datakey(ino0, n)