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Proof step 9 from proof overwrite-pcache-empty (previous step)

files[ino] = mkfile(m, md, m0, content), ino ∈ files ⊦ content ⊕ mkcontent(ino, ∅) = content

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ content = content0 ↔ (∀ n. (n ∈ content ↔ n ∈ content0) ∧ content[n] = content0[n])
Proof step 11:
files[ino] = mkfile(m, md, m0, content), ino ∈ files ⊦ ∀ n. (n ∈ content ⊕ mkcontent(ino, ∅) ↔ n ∈ content) ∧ (content ⊕ mkcontent(ino, ∅))[n] = content[n]

Rule argument

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

Additional information

Used terms: content, content ⊕ mkcontent(ino, ∅)