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Proof step 21 from proof nextli-lemma (previous step)

lfgen(0)(0) = [], m0 < n1, n1 ≤ n0, m0 < n0, ∀ lfgen, n1, n0, nextli. lfgen(0)(0) = [] ∧ m0 ≤ n1 ∧ n1 ≤ n0 ∧ m0 ≤ n0 ∧ (∀ 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), n1 = 0, n0 = 0

User applied rule all left

And obtained the following new goals

Proof step 22:
lfgen(0)(0) = [], m0 < n1, n1 ≤ n0, m0 < n0, lfgen(0)(0) = [] ∧ m0 ≤ n1 ∧ n1 ≤ n0 ∧ m0 ≤ n0 ∧ (∀ 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), n1 = 0, n0 = 0

Rule argument

pos: left 5 terms: lfgen, n1, n0, nextli abort: F discard: T computed: F

Additional information

Used terms: lfgen, n1, n0, nextli