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Proof step 2 from proof to-unwind-begin (previous step)

⌜n⌝ < # σ ⊦ σ to n + 1 = ⌜σ[0] '⌝ + (tl(σ) to n)

User applied rule insert elim lemma

And obtained the following new goals

Rule argument

spec: stream inst: name: elim-hd-tl seq: ⊦ σ ≠ [] → (a = hd(σ) ∧ σ0 = tl(σ) ↔ σ = a + σ0) subst: [σ, a, σ0] → [σ, a, σ0] flags: rewrite, current

Additional information

Used simplifier rules: size-empty: ⊦ # [] = ⌜0⌝ ;%cons-append: ⊦ a + σ = ⌜a '⌝ + σ;%to-succ-cons: ⊦ ⌜a '⌝ + σ to n + 1 = a + (σ to n);%append-assoc: ⊦ (σ + σ1) + σ2 = σ + σ1 + σ2;%get-cons-zero: ⊦ (⌜a '⌝ + σ)[0] = a;%append-cancel-l: ⊦ ⌜x⌝ + σ0 = ⌜x⌝ + σ1 ↔ σ0 = σ1;%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2%less-fin: ⊦ ⌜m⌝ < ⌜n⌝ ↔ m < n; from specification nat-inf%zero-01: ⊦ ¬ m < 0; from specification nat-basic1 Used terms: σ, a, σ0