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Proof step 11 from proof cleanup-lpt-n-at (previous step)

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

Heuristic weak cut applied rule cut formula

And closed the goal!

Rule argument

fma: m = n0

Additional information

Used simplifier rules: cleanup-lpt-n-size: n ≤ # lpt ⊦ # cleanup-lpt(lpt, n) = # lpt;% ⊦ m ≠ n → lpt[n, lp][m] = lpt[m]; (s)% ⊦ m ≠ n → (m ≤ n ↔ m < n); (s)% ⊦ m < n → m ≤ n; (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m < n → (n ≤ m ↔ false); (s)%m < # lpt ⊦ lpt[m, lp][m] = lp; (s)% ⊦ m ≤ m; (s)% ⊦ ¬ n < n; (s)%⊦ mklp(m, m0, lpf, m1) = mklp(m2, m3, lpf0, m4) ↔ m = m2 ∧ m0 = m3 ∧ lpf = lpf0 ∧ m1 = m4; (ws) Used formulas: m = n0