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Proof step 32 from proof replay-lpt-at (previous step)

lpt[n0] = mklp(0, m4, lpf0, m5), lpt[m] = mklp(m0, m1, lpf, m2), mklp(m0, m1, lpf, m2) = (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))) ), n0 < # lpt, m < # lpt, m ≤ n0 ⊦ replay-lpt(lpt, nx, n0)[n0, mklp(0, 0, LP_FREE, m5)][m] = replay-lpt(lpt, nx, n0)[m], lpf0 = LP_FREE, n0 ∈ nx

User applied rule case distinction

And obtained the following new goals

Proof step 33:
lpt[m] = mklp(m0, m1, lpf, m2), lpt[n0] = mklp(0, m4, lpf0, m5), mklp(m0, m1, lpf, m2) = mklp(m0, m1, lpf, m2), m < # lpt, n0 < # lpt, m ≤ n0, lpf = LP_FREE ∨ m ∈ nx ⊦ replay-lpt(lpt, nx, n0)[n0, mklp(0, 0, LP_FREE, m5)][m] = replay-lpt(lpt, nx, n0)[m], lpf0 = LP_FREE, n0 ∈ nx
Proof step 36:
lpt[m] = mklp(m0, m1, lpf, m2), lpt[n0] = mklp(0, m4, lpf0, m5), 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))), m < # lpt, n0 < # lpt, m ≤ n0 ⊦ replay-lpt(lpt, nx, n0)[n0, mklp(0, 0, LP_FREE, m5)][m] = replay-lpt(lpt, nx, n0)[m], lpf = LP_FREE, lpf0 = LP_FREE, n0 ∈ nx, m ∈ nx

Rule argument

pos: left 3

Proof step 32 from proof replay-lpt-at (previous step)

User applied rule case distinction

And obtained the following new goals

Rule argument

Additional information