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Proof step 22 from proof nextli-lemma (previous step)

lfgen(0)(0) = [], m0 < n1, m0 < n0, n1 ≤ n0, ∀ n. lfgen(n)(0) = [] ∧ (∀ m. m < n → lfgen(n)(m + 1) = nextli(lfgen(n)(m))), ∀ lfgen, n0, n1, nextli. lfgen(0)(0) = [] ∧ m0 ≤ n0 ∧ n1 ≤ n0 ∧ m0 ≤ n1 ∧ (∀ n. lfgen(n)(0) = [] ∧ (∀ m. m < n → lfgen(n)(m + 1) = nextli(lfgen(n)(m)))) → lfgen(n1)(m0) = lfgen(n0)(m0) ⊦ lfgen(n1)(m0 + 1) = lfgen(n0)(m0 + 1)

User applied rule all left

And obtained the following new goals

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

Rule argument

pos: left 6 terms: lfgen, n0, n1, nextli abort: F discard: T computed: F

Additional information

Used terms: lfgen, n0, n1, nextli