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Proof step 52 from proof nextl-nextj-lemma-butlast (previous step)

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)

User applied rule cut formula

And obtained the following new goals

Proof step 53:
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, (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

fma: n = m0 + 1

Additional information

Used simplifier rules: lep-02: ⊦ m + n ≤ m + n0 ↔ n ≤ n0; from specification nat%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2%eq-01: ⊦ m + n = m + n0 ↔ n = n0; from specification nat-basic2 Used formulas: n = m0 + 1