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Proof step 51 from proof nextl-nextj-lemma-butlast (previous step)

lf(0) = a ', ∀ n. n ≤ m0 → lf(n + 1) = nextl(jj(n), lf(n).last) ∧ jj(n + 1) = nextj(jj(n), lf(n).last) ⊦ (0 = m0 + 2 ⊃ nextl(jj(m0 + 1), lf(m0 + 1).last);lf(0)) = a ' ∧ (0 = m0 + 2 ⊃ nextj(jj(m0 + 1), lf(m0 + 1).last);jj(0)) = jj(0) ∧ (∀ n. n ≤ m0 + 1 → (n + 1 = m0 + 2 ⊃ nextl(jj(m0 + 1), lf(m0 + 1).last);lf(n + 1)) = nextl((n = m0 + 2 ⊃ nextj(jj(m0 + 1), lf(m0 + 1).last);jj(n)), (n = m0 + 2 ⊃ nextl(jj(m0 + 1), lf(m0 + 1).last);lf(n)).last) ∧ (n + 1 = m0 + 2 ⊃ nextj(jj(m0 + 1), lf(m0 + 1).last);jj(n + 1)) = nextj((n = m0 + 2 ⊃ nextj(jj(m0 + 1), lf(m0 + 1).last);jj(n)), (n = m0 + 2 ⊃ nextl(jj(m0 + 1), lf(m0 + 1).last);lf(n)).last))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 52:
lf(0) = a ', n ≤ m0 + 1, ∀ n. n ≤ m0 → lf(n + 1) = nextl(jj(n), lf(n).last) ∧ jj(n + 1) = nextj(jj(n), lf(n).last) ⊦ (n = m0 + 1 ⊃ nextl(jj(m0 + 1), lf(m0 + 1).last);lf(n + 1)) = nextl((n = m0 + 2 ⊃ nextj(jj(m0 + 1), lf(m0 + 1).last);jj(n)), (n = m0 + 2 ⊃ nextl(jj(m0 + 1), lf(m0 + 1).last);lf(n)).last) ∧ (n = m0 + 1 ⊃ nextj(jj(m0 + 1), lf(m0 + 1).last);jj(n + 1)) = nextj((n = m0 + 2 ⊃ nextj(jj(m0 + 1), lf(m0 + 1).last);jj(n)), (n = m0 + 2 ⊃ nextl(jj(m0 + 1), lf(m0 + 1).last);lf(n)).last)

Rule argument

Additional information

Used simplifier rules: add-num-01: n < n0 ⊦ m + (* n) = m0 + (* n0) ↔ m = m0 + (n0 - n); from specification nat%c: ⊦ m + n = n + m; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%add-num-03: n < n0 ⊦ (* n) ≠ m0 + (* n0); from specification nat