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Proof step 2 from proof P-ext (previous step)

∀ n. (n ∈ content ↔ datakey(ino, n) ∈ ri) ∧ (n ∈ content → content[n] = fs[ri[datakey(ino, n)]].data) ⊦ content = abs-content(ino, fs, ri)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ content = content0 ↔ (∀ n. (n ∈ content ↔ n ∈ content0) ∧ (n ∈ content → content[n] = content0[n]))
Proof step 4:
∀ n. (n ∈ content ↔ datakey(ino, n) ∈ ri) ∧ (n ∈ content → content[n] = fs[ri[datakey(ino, n)]].data) ⊦ ∀ n. (n ∈ content ↔ n ∈ abs-content(ino, fs, ri)) ∧ (n ∈ content → content[n] = abs-content(ino, fs, ri)[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] → [abs-content(ino, fs, ri), content] flags: <all paths>

Additional information

Used terms: abs-content(ino, fs, ri), content