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Proof step 33 from proof nextl-nextj-lemma-butlast (previous step)

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

User applied rule all left

And obtained the following new goals

Proof step 34:
lfgen(n)(0) = a ', m0 < n, m0 + 1 < n, ∀ n. m0 ≤ n → lfgen(n)(m0) = lfgen(m0)(m0) ∧ iigen(n)(m0) = iigen(m0)(m0), m0 ≤ n → lfgen(n)(m0 + 1) = nextl(iigen(n)(m0), lfgen(n)(m0).last) ∧ iigen(n)(m0 + 1) = nextj(iigen(n)(m0), lfgen(n)(m0).last), ∀ n0. n0 ≤ n → lfgen(n)(n0 + 1) = nextl(iigen(n)(n0), lfgen(n)(n0).last) ∧ iigen(n)(n0 + 1) = nextj(iigen(n)(n0), lfgen(n)(n0).last), ∀ m. lfgen(m)(0) = a ' ∧ iigen(m)(0) = iigen(n)(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)) ⊦ n = m0 + 1, n = 0, lfgen(n)(m0 + 1) = lfgen(m0 + 1)(m0 + 1) ∧ iigen(n)(m0 + 1) = iigen(m0 + 1)(m0 + 1)

Rule argument

pos: left 5 terms: m0 abort: F discard: F computed: T

Additional information

Used terms: m0