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Proof step 4 from proof eq-leninv (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ stutf(nσ) → (leninv(nσ) = ⌜0⌝ ↔ nσ = ⌜λ n. 0⌝ )
Proof step 6:
stutf(nσ), nσ[n] = 0, ⌜n⌝ < # nσ, stutf(nσ) ⊦ nσ = ⌜λ n. 0⌝ ↔ # nσ = ∞ ∧ (∀ m. n < m ∧ ⌜m⌝ < # nσ → nσ[m] = 0)

Rule argument

spec: inst: name: leninv-zero seq: ⊦ stutf(nσ) → (leninv(nσ) = ⌜0⌝ ↔ nσ = ⌜λ n. 0⌝ ) subst: [nσ] → [nσ] flags: rewrite, current

Additional information

Used terms: nσ