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Proof step 8 from proof cleanup-lpt-n-at (previous step)

lpt[n0] = mklp(m3, m4, lpf0, m5), lpt[m] = mklp(m0, m1, lpf, m2), m < # lpt, n0 < # lpt, m ≤ n0, lpt[m] = mklp(m0, m1, lpf, m2) ∧ m < n0 ∧ m < # lpt ∧ n0 ≤ # lpt → cleanup-lpt(lpt, n0)[m] = (m0 = 0 ∧ lpf ≠ LP_FREE ⊃ mklp(0, 0, LP_FREE, m2);mklp(m0, m1, lpf, m2)) ⊦ (m3 = 0 ∧ lpf0 ≠ LP_FREE ⊃ cleanup-lpt(lpt, n0)[n0, mklp(0, 0, LP_FREE, m5)];cleanup-lpt(lpt, n0))[m] = (m0 = 0 ∧ lpf ≠ LP_FREE ⊃ mklp(0, 0, LP_FREE, m2);mklp(m0, m1, lpf, m2))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
lpt[m] = mklp(m0, m1, lpf, m2), lpt[n0] = mklp(m3, m4, lpf0, m5), n0 < # lpt, m < # lpt, m ≤ n0, m < n0 → cleanup-lpt(lpt, n0)[m] = (m0 = 0 ∧ lpf ≠ LP_FREE ⊃ mklp(0, 0, LP_FREE, m2);mklp(m0, m1, lpf, m2)) ⊦ (m3 = 0 ∧ lpf0 ≠ LP_FREE ⊃ cleanup-lpt(lpt, n0)[n0, mklp(0, 0, LP_FREE, m5)];cleanup-lpt(lpt, n0))[m] = (m0 = 0 ∧ lpf ≠ LP_FREE ⊃ mklp(0, 0, LP_FREE, m2);mklp(m0, m1, lpf, m2))

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → m ≤ n; (s)