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Proof step 11 from proof leq-leninv (previous step)

leninv(nσ) = ⌜n1⌝ + ⌜1⌝ , ⌜n⌝ < # nσ, n1 + 1 < nσ[n], stutf(nσ) ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 12:
⊦ stutf(nσ) → (leninv(nσ) = ⌜n⌝ + ⌜1⌝ ↔ (# nσ = ∞ ⊃ ∃ m. nσ[m] = n ∧ (∀ m0. m < m0 → nσ[m0] = n + 1);nσ[(# nσ).n - 1] = n))
Proof step 13:
n1 + 1 < nσ[n], ⌜n⌝ < # nσ, stutf(nσ), (# nσ = ∞ ⊃ ∃ m. nσ[m] = n1 ∧ (∀ m0. m < m0 → nσ[m0] = n1 + 1);nσ[(# nσ).n - 1] = n1) ⊦

Rule argument

spec: <toplevel> name: leninv-succ seq: ⊦ stutf(nσ) → ( leninv(nσ) = ⌜n⌝ + ⌜1⌝ ↔ (# nσ = ∞ ⊃ ∃ m. nσ[m] = n ∧ (∀ m0. m < m0 → nσ[m0] = n + 1) ;nσ[(# nσ).n - 1] = n )) subst: [n, nσ] → [n1, nσ] flags: <all paths>

Additional information

Used terms: n1, nσ