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Proof step 10 from proof leninv-zero (previous step)

stutf(nσ), ∀ m. (∃ m0. ⌜m0⌝ < # nσ ∧ nσ[m0] = m - 1 ∧ (# nσ ≠ ∞ ∨ ¬(∀ m1. m0 < m1 → nσ[m1] = m - 1))) → m = 0 ⊦ # nσ = # ⌜λ n. 0⌝ ∧ (∀ n. ⌜n⌝ < # nσ → nσ[n] = ⌜λ n. 0⌝ [n])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 11:
stutf(nσ), ∀ m. (∃ m0. ⌜m0⌝ < # nσ ∧ nσ[m0] = m - 1 ∧ (# nσ ≠ ∞ ∨ ¬(∀ m1. m0 < m1 → nσ[m1] = m - 1))) → m = 0 ⊦ # nσ = ∞ ∧ (⌜n⌝ < # nσ → nσ[n] = 0)

Rule argument

Additional information

Used simplifier rules: sel-inf: ⊦ ⌜nnf⌝ [n] = nnf(n); from specification stream[natstream]%size-inf: ⊦ # ⌜nnf⌝ = ∞; from specification stream[natstream]