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Proof step 3 from proof replay-lpt-at (previous step)

lpt[m] = mklp(m0, m1, lpf, m2), m < # lpt, m < n, n ≤ # lpt ⊦ replay-lpt(lpt, nx, n)[m] = (lpf = LP_FREE ∨ m ∈ nx ⊃ lpt[m];(lpf = LP_INDEX_NODES ∧ m0 ≠ 0 ⊃ lpt[m].size:= LEB_SIZE;(m0 = 0 ⊃ mklp(0, 0, LP_FREE, m2);lpt[m])))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
lpt[m] = mklp(m0, m1, lpf, m2), m < # lpt, m < n, n ≤ # lpt ⊦ replay-lpt(lpt, nx, n)[m] = (lpf = LP_FREE ∨ m ∈ nx ⊃ mklp(m0, m1, lpf, m2) ;(lpf = LP_INDEX_NODES ∧ m0 ≠ 0 ⊃ mklp(m0, LEB_SIZE, LP_INDEX_NODES, m2);(m0 = 0 ⊃ mklp(0, 0, LP_FREE, m2);mklp(m0, m1, lpf, m2))) )

Rule argument

Additional information

Used simplifier rules: ⊦ mklp(m, m0, lpf, m1).size:= m3 = mklp(m, m3, lpf, m1); (s)