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Proof step 92 from proof leninv-succ (previous step)

stutf(nσ) ⊦ ∀ n. # nσ ≠ ⌜n⌝ , (∃ m. ⌜m⌝ < # nσ ∧ nσ[m] = n) ∧ (∀ m. (m ≠ 0 → (∃ m0. ⌜m0⌝ < # nσ ∧ nσ[m0] = m - 1)) → ¬ n + 1 < m) ↔ nσ[(# nσ).n - 1] = n

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 93:
# nσ = ⌜n0⌝ , stutf(nσ) ⊦ (∃ m. m < n0 ∧ nσ[m] = n) ∧ (∀ m. (m ≠ 0 → (∃ m0. m0 < n0 ∧ nσ[m0] = m - 1)) → ¬ n + 1 < m) ↔ nσ[n0 - 1] = n

Rule argument

Additional information

Used simplifier rules: sel: ⊦ ⌜m⌝ .n = m; from specification nat-inf-basic%less-fin: ⊦ ⌜m⌝ < ⌜n⌝ ↔ m < n; from specification nat-inf