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Proof step 51 from proof lim-unique (previous step)

∞ = # σ, mon(σσ), ∀ m. ¬ # σ0 < ⌜m⌝ → (∃ n. ⌜n⌝ < # σσ ∧ (∃ σ1. (σ0 to m) + σ1 = σσ[n])), ∀ n. ⌜n⌝ < # σσ → (∃ σ1. σσ[n] + σ1 = σ0), ∀ n. ⌜n⌝ < # σσ → (∃ σ1. σσ[n] + σ1 = σ), ∀ m. ∃ n. ⌜n⌝ < # σσ ∧ (∃ σ1. (σ to m) + σ1 = σσ[n]) ⊦ σσ = [], ∞ = # σ0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 52:
⊦ n∞ ≠ ∞ ↔ (∃ n. n∞ = ⌜n⌝ )
Proof step 53:
∞ = # σ, mon(σσ), ∀ m. ¬ # σ0 < ⌜m⌝ → (∃ n. ⌜n⌝ < # σσ ∧ (∃ σ1. (σ0 to m) + σ1 = σσ[n])), ∀ n. ⌜n⌝ < # σσ → (∃ σ1. σσ[n] + σ1 = σ0), ∀ n. ⌜n⌝ < # σσ → (∃ σ1. σσ[n] + σ1 = σ), ∀ m. ∃ n. ⌜n⌝ < # σσ ∧ (∃ σ1. (σ to m) + σ1 = σσ[n]) ⊦ σσ = [], ∀ n. # σ0 ≠ ⌜n⌝

Rule argument

spec: nat-inf-basic inst: name: notinf-fin seq: ⊦ n∞ ≠ ∞ ↔ (∃ n. n∞ = ⌜n⌝ ) subst: [n∞] → [# σ0] flags: rewrite

Additional information

Used terms: # σ0