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Proof step 6 from proof eq-leninv (previous step)

stutf(nσ), nσ[n] = 0, ⌜n⌝ < # nσ, stutf(nσ) ⊦ nσ = ⌜λ n. 0⌝ ↔ # nσ = ∞ ∧ (∀ m. n < m ∧ ⌜m⌝ < # nσ → nσ[m] = 0)

User applied rule case distinction

And obtained the following new goals

Proof step 7:
# nσ = ∞ ∧ (∀ m. n < m ∧ ⌜m⌝ < # nσ → nσ[m] = 0), stutf(nσ), nσ[n] = 0, ⌜n⌝ < # nσ, stutf(nσ) ⊦ nσ = ⌜λ n. 0⌝

Rule argument

pos: right 1

Additional information

Used simplifier rules: sel-inf: ⊦ ⌜nnf⌝ [n] = nnf(n); from specification stream[natstream]%size-inf: ⊦ # ⌜nnf⌝ = ∞; from specification stream[natstream]%less-inf2: ⊦ ⌜m⌝ < ∞; from specification nat-inf