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Proof step 22 from proof nextl-lemma-butlast-nonempty (previous step)

∀ lfgen, a, n1, n0, nextl. lfgen(0)(0) = a ' ∧ m0 ≤ n1 ∧ n1 ≤ n0 ∧ m0 ≤ n0 ∧ (∀ n. lfgen(n)(0) = a ' ∧ (∀ m. m < n → lfgen(n)(m + 1) = nextl(m, lfgen(n)(m).last) ∧ lfgen(n)(m) ≠ [])) ∧ (∀ n, a. nextl(n, a) ≠ []) → lfgen(n1)(m0) = lfgen(n0)(m0), lfgen(0)(0) = a ', m0 +1 ≤ n1, n1 ≤ n0, m0 +1 ≤ n0, ∀ n. lfgen(n)(0) = a ' ∧ (∀ m. m < n → lfgen(n)(m + 1) = nextl(m, lfgen(n)(m).last) ∧ lfgen(n)(m) ≠ []), ∀ n, a. nextl(n, a) ≠ [] ⊦ lfgen(n1)(m0 +1) = lfgen(n0)(m0 +1)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 23:
lfgen(0)(0) = a ', m0 < n1, n1 ≤ n0, m0 < n0, ∀ lfgen, a, n1, n0, nextl. lfgen(0)(0) = a ' ∧ m0 ≤ n1 ∧ n1 ≤ n0 ∧ m0 ≤ n0 ∧ (∀ n. lfgen(n)(0) = a ' ∧ (∀ m. m < n → lfgen(n)(m + 1) = nextl(m, lfgen(n)(m).last) ∧ lfgen(n)(m) ≠ [])) ∧ (∀ n, a. nextl(n, a) ≠ []) → lfgen(n1)(m0) = lfgen(n0)(m0), ∀ n. lfgen(n)(0) = a ' ∧ (∀ m. m < n → lfgen(n)(m + 1) = nextl(m, lfgen(n)(m).last) ∧ lfgen(n)(m) ≠ []), ∀ n, a. nextl(n, a) ≠ [] ⊦ lfgen(n1)(m0 + 1) = lfgen(n0)(m0 + 1), n1 = 0, n0 = 0

Rule argument

Additional information

Used simplifier rules: fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic1%c: ⊦ m + n = n + m; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%succ-01: ⊦ m + 1 ≤ n ↔ m < n; from specification nat%succ: ⊦ m +1 = m + 1; from specification nat-basic2