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Proof step 10 from proof nextl-nextj-lemma-butlast (previous step)

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

User applied rule all left

And obtained the following new goals

Proof step 11:
lfgen(0)(0) = a ', iigen(0)(1) = nextj(iigen(0)(0), a), lfgen(0)(1) = nextl(iigen(0)(0), a), ∀ m, n. m ≤ n → lfgen(n)(m) = lfgen(m)(m) ∧ iigen(n)(m) = iigen(m)(m), lfgen(n + 1)(0) = a ' ∧ iigen(n + 1)(0) = iigen(0)(0) ∧ (∀ n0. n0 ≤ n + 1 → lfgen(n + 1)(n0 + 1) = nextl(iigen(n + 1)(n0), lfgen(n + 1)(n0).last) ∧ iigen(n + 1)(n0 + 1) = nextj(iigen(n + 1)(n0), lfgen(n + 1)(n0).last)), ∀ m. lfgen(m)(0) = a ' ∧ iigen(m)(0) = iigen(0)(0) ∧ (∀ 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)) ⊦ lfgen(n + 1)(n + 1) = nextl(iigen(n)(n), lfgen(n)(n).last) ∧ iigen(n + 1)(n + 1) = nextj(iigen(n)(n), lfgen(n)(n).last)

Rule argument

pos: left 5 terms: n + 1 abort: F discard: F computed: F

Additional information

Used terms: n + 1