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Proof step 54 from proof leninv-inf (previous step)

∀ n. ∃ n0. n < n0 ∧ (∃ m. ⌜m⌝ < # nσ ∧ nσ[m] = n0 - 1), # nσ = ⌜n⌝ , stutf(nσ) ⊦

User applied rule constructor cut

And obtained the following new goals

Proof step 55:
n = n1 +1, ∀ n. ∃ n0. n < n0 ∧ (∃ m. ⌜m⌝ < # nσ ∧ nσ[m] = n0 - 1), # nσ = ⌜n⌝ , stutf(nσ) ⊦

Rule argument

var: n

Additional information

Used simplifier rules: stutf-nonempty: ⊦ stutf(nσ) → (¬ nσ ≠ [] ↔ false);%nat freely generated by 0, +1;;%size-empty-equiv: ⊦ # nσ = ⌜0⌝ ↔ nσ = []; from specification stream[natstream]