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Proof step 128 from proof lim-exists (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 129:
⊦ n∞ ≠ ∞ ↔ (∃ n. n∞ = ⌜n⌝ )
Proof step 130:
mon(σσ) ⊦ ∀ n. # σσ ≠ ⌜n⌝ , σσ = [], ∃ σ. (∀ n. ⌜n⌝ < # σσ → (∃ σ1. σσ[n] + σ1 = σ)) ∧ (∀ m. ¬ # σ < ⌜m⌝ → (∃ n. ⌜n⌝ < # σσ ∧ (∃ σ1. (σ to m) + σ1 = σσ[n])))

Rule argument

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

Additional information

Used terms: # σσ