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Proof step 8 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⌝

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ nσ = nσ0 ↔ # nσ = # nσ0 ∧ (∀ n. ⌜n⌝ < # nσ → nσ[n] = nσ0[n])
Proof step 10:
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])

Rule argument

spec: stream inst: natstream name: extensionality seq: ⊦ nσ = nσ0 ↔ # nσ = # nσ0 ∧ (∀ n. ⌜n⌝ < # nσ → nσ[n] = nσ0[n]) subst: [nσ0, nσ] → [⌜λ n. 0⌝ , nσ] flags: rewrite

Additional information

Used terms: ⌜λ n. 0⌝ , nσ