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Proof step 43 from proof lim-unique (previous step)

# σ = # σ0, # σ1 + # σ3 = # σ2, (σ to n) + σ1 to n = (σ0 to n) + σ2 to n, mon(σσ), ⌜n0⌝ < # σσ, ⌜n1⌝ < # σσ, ∀ n. ⌜n⌝ < # σσ → (∃ σ1. σσ[n] + σ1 = σ), ∀ n. ⌜n⌝ < # σσ → (∃ σ1. σσ[n] + σ1 = σ0) ⊦ σσ = [], σ to n = σ0 to n, # σ0 < ⌜n⌝

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 44:
⊦ ¬ # σ < ⌜n⌝ → σ + σ0 to n = σ to n
Proof step 45:
¬ #(σ to n) < ⌜n⌝ , # σ = # σ0, # σ1 + # σ3 = # σ2, σ to n to n = (σ0 to n) + σ2 to n, mon(σσ), ⌜n0⌝ < # σσ, ⌜n1⌝ < # σσ, ∀ n. ⌜n⌝ < # σσ → (∃ σ1. σσ[n] + σ1 = σ), ∀ n. ⌜n⌝ < # σσ → (∃ σ1. σσ[n] + σ1 = σ0) ⊦ σσ = [], σ to n = σ0 to n, # σ0 < ⌜n⌝

Rule argument

spec: stream inst: name: append-to-ls seq: ⊦ ¬ # σ < ⌜n⌝ → σ + σ0 to n = σ to n subst: [n, σ0, σ] → [n, σ1, σ to n] flags: rewrite

Additional information

Used simplifier rules: size-to: ¬ # σ < ⌜n⌝ ⊦ #(σ to n) = ⌜n⌝ ; from specification stream%less-fin: ⊦ ⌜m⌝ < ⌜n⌝ ↔ m < n; from specification nat-inf%ref-1: ⊦ ¬ n < n; from specification nat-basic1 Used terms: n, σ1, σ to n