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Proof step 25 from proof inv-inverts-last (previous step)

# nσ = ⌜n⌝ + ⌜1⌝ , leninv(nσ) = ⌜n1⌝ , stutf(nσ) ⊦ ((λ m. max∞(λ n0. ¬ n < n0 ∧ nσ[n0] = m).n) to n1)[nσ[n]] = n

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 26:
m < n ⊦ (nnf to n)[m] = nnf(m)
Proof step 27:
¬ nσ[n] < n1, # nσ = ⌜n⌝ + ⌜1⌝ , leninv(nσ) = ⌜n1⌝ , stutf(nσ) ⊦ ((λ m. max∞(λ n0. ¬ n < n0 ∧ nσ[n0] = m).n) to n1)[nσ[n]] = n
Proof step 32:
nσ[n] < n1, # nσ = ⌜n⌝ + ⌜1⌝ , leninv(nσ) = ⌜n1⌝ , stutf(nσ) ⊦ max∞(λ n0. ¬ n < n0 ∧ nσ[n0] = nσ[n]).n = n

Rule argument

spec: stream inst: natstream name: get-infto seq: m < n ⊦ (nnf to n)[m] = nnf(m) subst: [m, n, nnf] → [nσ[n], n1, λ m. max∞(λ n0. ¬ n < n0 ∧ nσ[n0] = m).n] flags: rewrite

Additional information

Used terms: nσ[n], n1, λ m. max∞(λ n0. ¬ n < n0 ∧ nσ[n0] = m).n