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Proof step 17 from proof nextl-lemma-butlast-nonempty (previous step)

lfgen(0)(0) = a ', m ≤ n1, n1 ≤ n0, m ≤ 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)(m) = lfgen(n0)(m)

User applied rule structural induction

And obtained the following new goals

Proof step 18:
lfgen(0)(0) = a ', 0 ≤ n1, n1 ≤ n0, 0 ≤ 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)(0) = lfgen(n0)(0)
Proof step 22:
∀ 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)

Rule argument

indvar: m

Additional information

Used simplifier rules: nat freely generated by 0, +1;;