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Proof step 3 from proof upto-less (previous step)

n ≤ m ⊦ (content upto m) upto n = content upto n

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ content = content0 ↔ (∀ n. (n ∈ content ↔ n ∈ content0) ∧ (n ∈ content → content[n] = content0[n]))
Proof step 5:
n ≤ m ⊦ ∀ n0. (n0 ∈ (content upto m) upto n ↔ n0 ∈ content upto n) ∧ (n0 ∈ (content upto m) upto n → ((content upto m) upto n)[n0] = (content upto n)[n0])

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 upto n, (content upto m) upto n] flags: <all paths>

Additional information

Used terms: content upto n, (content upto m) upto n