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Proof step 142 from proof overwrite-write-page-clean (previous step)

files[ino] = mkfile(m2, md0, m3, content0), icache[ino] = mkientry(boolvar, mkinode(m0, md, false, m1, m4, m5)), ino ∈ icache, ino ∈ files, n ∈ (content0 ⊕ mkcontent(ino, pcache))[m, buf] ⊦ datakey(ino, n) = datakey(ino, m), n ∈ content0, datakey(ino, n) ∈ pcache

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 143:
⊦ n ∈ content[n0, buf] ↔ n = n0 ∨ n ∈ content

Rule argument

spec: store, inst: file-content name: In-insert seq: ⊦ n ∈ content[n0, buf] ↔ n = n0 ∨ n ∈ content subst: [buf, n0, content, n] → [buf, m, content0 ⊕ mkcontent(ino, pcache), 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; Used terms: buf, m, content0 ⊕ mkcontent(ino, pcache), n