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

∀ lfgen, a, iigen, n0, nextl, nextj. (∀ m. lfgen(m)(0) = a ' ∧ iigen(m)(0) = n0 ∧ (∀ n. n ≤ m → lfgen(m)(n + 1) = nextl(iigen(m)(n), lfgen(m)(n).last) ∧ iigen(m)(n + 1) = nextj(iigen(m)(n), lfgen(m)(n).last))) → (∀ n. m0 ≤ n → lfgen(n)(m0) = lfgen(m0)(m0) ∧ iigen(n)(m0) = iigen(m0)(m0)), ∀ m. lfgen(m)(0) = a ' ∧ iigen(m)(0) = n0 ∧ (∀ n. n ≤ m → lfgen(m)(n + 1) = nextl(iigen(m)(n), lfgen(m)(n).last) ∧ iigen(m)(n + 1) = nextj(iigen(m)(n), lfgen(m)(n).last)) ⊦ ∀ n. m0 +1 ≤ n → lfgen(n)(m0 +1) = lfgen(m0 +1)(m0 +1) ∧ iigen(n)(m0 +1) = iigen(m0 +1)(m0 +1)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

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

Rule argument

Additional information

Used simplifier rules: 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