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Proof step 101 from proof leninv-succ (previous step)

¬ nσ[m] < nσ[m1], # nσ = ⌜m1⌝ + ⌜1⌝ , stutf(nσ), m ≤ m1, ∀ m0. (m0 ≠ 0 → (∃ m2. ¬ m1 < m2 ∧ nσ[m2] = m0 - 1)) → ¬ nσ[m] + 1 < m0 ⊦ nσ[m1] = nσ[m]

User applied rule insert lemma

And obtained the following new goals

Rule argument

spec: inst: name: monle-leq seq: ⊦ mon≤(nσ) ∧ m ≤ n ∧ ⌜n⌝ < # nσ → nσ[m] ≤ nσ[n] subst: [nσ, m, n] → [nσ, m, m1] flags: current, []

Additional information

Used simplifier rules: stutf-monle: ⊦ stutf(nσ) → (¬ mon≤(nσ) ↔ false);%neq-01: ⊦ m ≠ n → (¬ m < n ↔ n < m); from specification nat-basic1%add-assoc: ⊦ (n∞ + n∞1) + n∞2 = n∞ + n∞1 + n∞2; from specification nat-inf%add-comm: ⊦ n∞1 + n∞2 = n∞2 + n∞1; from specification nat-inf%inf-inseq-reduce: ⊦ n∞ = ⌜m⌝ + ⌜n0⌝ → (⌜n⌝ < n∞ ↔ n < m + n0); from specification nat-inf%s: ⊦ m < n + 1 ↔ ¬ n < m; from specification nat-basic2%ref-1: ⊦ ¬ n < n; from specification nat-basic1%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2%ls-le-simp: ⊦ m < n → (n ≤ m ↔ false); from specification nat Used terms: nσ, m, m1