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Proof step 47 from proof leninv-succ (previous step)

nσ[m0] = nσ[m1] + 1, # nσ = ∞, nσ[m1 + 1] = nσ[m0], nσ[m] = nσ[m1], nσ[m2] = nσ[m4] + 1, nσ[m0] ≤ nσ[m4], m < m0, stutf(nσ), m1 < m0, m ≤ m1, m1 < m2, m < m2, m4 ≤ m2, nσ[m1] < nσ[m4], m4 < m2 → nσ[m2] = nσ[m4] ⊦ m0 = 0, nσ[m2] = nσ[m0], m2 = 0, nσ[m4] = 0

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, m2, m4] flags: current, []

Additional information

Used simplifier rules: stutf-monle: ⊦ stutf(nσ) → (¬ mon≤(nσ) ↔ false);%anti: ⊦ m ≤ n → (n ≤ m ↔ m = n); from specification nat%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2%eq: ⊦ m = n + 1 → ¬ m ≤ n; from specification nat%less-inf2: ⊦ ⌜m⌝ < ∞; from specification nat-inf%lels-02: ⊦ m ≠ n → (m ≤ n ↔ m < n); from specification nat%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic1%eq: ⊦ m = m + n ↔ n = 0; from specification nat-basic2 Used terms: nσ, m2, m4