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Proof step 48 from proof leninv-succ (previous step)

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

User applied rule insert lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: monle-leq seq: ⊦ mon≤(nσ) ∧ m ≤ n ∧ ⌜n⌝ < # nσ → nσ[m] ≤ nσ[n] subst: [nσ, m, n] → [nσ, m2, m4]

Additional information

Used simplifier rules: stutf-monle: ⊦ stutf(nσ) → (mon≤(nσ) ↔ true);% ⊦ m ≤ n → (n ≤ m ↔ m = n); (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m = n + 1 → ¬ m ≤ n; (s)% ⊦ m = m + n ↔ n = 0; (s)% ⊦ m ≠ n → (m ≤ n ↔ m < n); (s)%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic Used terms: nσ, m2, m4