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Proof step 13 from proof lim-unique (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 14:
# σ = # σ0, (σ to n) + σ1 = σσ[n0], (σ0 to n) + σ2 = σσ[n1], mon(σσ), ⌜n0⌝ < # σσ, ⌜n1⌝ < # σσ, n1 < n0, ∀ n. ⌜n⌝ < # σσ → (∃ σ1. σσ[n] + σ1 = σ), ∀ n. ⌜n⌝ < # σσ → (∃ σ1. σσ[n] + σ1 = σ0) ⊦ σσ = [], σ to n = σ0 to n, n0 = 0, # σ0 < ⌜n⌝

Rule argument

Additional information

Used simplifier rules: f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic1%lels-01: ⊦ ¬ m ≤ n ↔ n < m; from specification nat