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Proof step 7 from proof at-pcache-overwrite-other (previous step)

files[ino] = mkfile(m, md, m0, content) ⊦ ino = key0.ino, content ⊕ mkcontent(ino, pcache[key0, pe]) = content ⊕ mkcontent(ino, pcache)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ content = content0 ↔ (∀ n. (n ∈ content ↔ n ∈ content0) ∧ (n ∈ content → content[n] = content0[n]))
Proof step 9:
files[ino] = mkfile(m, md, m0, content) ⊦ ino = key0.ino, ∀ n. (n ∈ content ⊕ mkcontent(ino, pcache[key0, pe]) ↔ n ∈ content ⊕ mkcontent(ino, pcache)) ∧ (n ∈ content ⊕ mkcontent(ino, pcache[key0, pe]) → (content ⊕ mkcontent(ino, pcache[key0, pe]))[n] = (content ⊕ mkcontent(ino, pcache))[n])

Rule argument

spec: store, inst: file-content name: k-Extension seq: ⊦ content = content0 ↔ (∀ n. (n ∈ content ↔ n ∈ content0) ∧ (n ∈ content → content[n] = content0[n])) subst: [content0, content] → [content ⊕ mkcontent(ino, pcache), content ⊕ mkcontent(ino, pcache[key0, pe])] flags: <all paths>

Additional information

Used terms: content ⊕ mkcontent(ino, pcache), content ⊕ mkcontent(ino, pcache[key0, pe])