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Proof step 11 from proof inv-ls-succ (previous step)

leninv(nσ) = ∞, ∞.n ≤ max∞(λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = n).n, stutf(nσ), (∀ n0. ∃ n1. n0 < n1 ∧ ⌜n1⌝ < # nσ ∧ nσ[n1] = n + 1) ∨ (∀ n0. ¬ ⌜n0⌝ < # nσ ∨ nσ[n0] ≠ n + 1) ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 12:
⊦ stutf(nσ) → (leninv(nσ) = ∞ ↔ # nσ = ∞ ∧ (∀ m. ∃ m0. m < m0 ∧ nσ[m] < nσ[m0]))
Proof step 13:
stutf(nσ), # nσ = ∞ ∧ (∀ m. ∃ m0. m < m0 ∧ nσ[m] < nσ[m0]), ∞.n ≤ max∞(λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = n).n, stutf(nσ), (∀ n0. ∃ n1. n0 < n1 ∧ ⌜n1⌝ < # nσ ∧ nσ[n1] = n + 1) ∨ (∀ n0. ¬ ⌜n0⌝ < # nσ ∨ nσ[n0] ≠ n + 1) ⊦

Rule argument

spec: inst: name: leninv-inf seq: ⊦ stutf(nσ) → ( leninv(nσ) = ∞ ↔ # nσ = ∞ ∧ (∀ m. ∃ m0. m < m0 ∧ nσ[m] < nσ[m0])) subst: [nσ] → [nσ] flags: rewrite, current

Additional information

Used terms: nσ