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Proof step 7 from proof extensionality-to (previous step)

# σ0 = # σ1, σ0 to n + 1 = σ1 to n + 1, ⌜n⌝ < # σ1, ∀ n. ¬ # σ1 < ⌜n⌝ → σ0 to n = σ1 to n ⊦ σ0[n] = σ1[n]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⌜n⌝ < # σ ⊦ σ to n + 1 = (σ to n) + ⌜σ[n] '⌝
Proof step 9:
⌜n⌝ < # σ0, # σ0 = # σ1, (σ0 to n) + ⌜σ0[n] '⌝ = σ1 to n + 1, ⌜n⌝ < # σ1, ∀ n. ¬ # σ1 < ⌜n⌝ → σ0 to n = σ1 to n ⊦ σ0[n] = σ1[n]

Rule argument

spec: stream inst: name: to-unwind-end seq: ⌜n⌝ < # σ ⊦ σ to n + 1 = (σ to n) + ⌜σ[n] '⌝ subst: [n, σ] → [n, σ0] flags: rewrite, current

Additional information

Used simplifier rules: lsle-trans: ⊦ n∞ < n∞1 ∧ ¬ n∞2 < n∞1 → n∞ < n∞2; (forward) from specification nat-inf%lels-trans: ⊦ ¬ n∞1 < n∞ ∧ n∞1 < n∞2 → n∞ < n∞2; (forward) from specification nat-inf Used terms: n, σ0