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Proof step 12 from proof extensionality-to (previous step)

⌜n⌝ < # σ1, # σ0 = # σ1, (σ0 to n) + ⌜σ0[n] '⌝ = (σ1 to n) + ⌜σ1[n] '⌝ , ⌜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

Rule argument

spec: stream inst: name: append-split seq: ⊦ finp(σ) ∧ # σ = # σ1 → (σ + σ0 = σ1 + σ2 ↔ σ = σ1 ∧ σ0 = σ2) subst: [σ2, σ1, σ0, σ] → [⌜σ1[n] '⌝ , σ1 to n, ⌜σ0[n] '⌝ , σ0 to n] flags: rewrite, current

Additional information

Used simplifier rules: fin-to: ⊦ finp(σ to m);%size-to: ¬ # σ < ⌜n⌝ ⊦ #(σ to n) = ⌜n⌝ ;%size-to: ¬ # σ < ⌜n⌝ ⊦ #(σ to n) = ⌜n⌝ ;%ls-le: ⊦ n∞ < n∞0 → ¬ n∞0 < n∞; from specification nat-inf%inj: ⊦ ⌜m⌝ = ⌜m0⌝ ↔ m = m0; from specification nat-inf-basic%inj-02: ⊦ ⌜x⌝ = ⌜x0⌝ ↔ x = x0; from specification stream-basic%c-04: ⊦ a ' = b ' ↔ a = b; from specification list Used terms: ⌜σ1[n] '⌝ , σ1 to n, ⌜σ0[n] '⌝ , σ0 to n