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Proof step 2 from proof inv-inverts (previous step)

nσ[n + 1] = nσ[n] + 1, stutf(nσ), ⌜n⌝ + ⌜1⌝ < # nσ ⊦ inv(nσ)[nσ[n]] = n

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ stutf(nσ) → inv(nσ) = (leninv(nσ) = ∞ ⊃ ⌜λ m. max∞(λ n. ⌜n⌝ < # nσ ∧ nσ[n] = m).n⌝ ;⌜λ m. max∞(λ n. ⌜n⌝ < # nσ ∧ nσ[n] = m).n⌝ to leninv(nσ).n)
Proof step 4:
stutf(nσ), nσ[n + 1] = nσ[n] + 1, stutf(nσ), ⌜n⌝ + ⌜1⌝ < # nσ ⊦ (leninv(nσ) = ∞ ⊃ ⌜λ m. max∞(λ n. ⌜n⌝ < # nσ ∧ nσ[n] = m).n⌝ ;⌜λ m. max∞(λ n. ⌜n⌝ < # nσ ∧ nσ[n] = m).n⌝ to leninv(nσ).n)[nσ[n]] = n

Rule argument

spec: inst: name: inv-def seq: ⊦ stutf(nσ) → inv(nσ) = (leninv(nσ) = ∞ ⊃ ⌜λ m. max∞(λ n. ⌜n⌝ < # nσ ∧ nσ[n] = m).n⌝ ; ⌜λ m. max∞(λ n. ⌜n⌝ < # nσ ∧ nσ[n] = m).n⌝ to leninv(nσ).n ) subst: [nσ] → [nσ] flags: rewrite, current

Additional information

Used terms: nσ