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Proof step 12 from proof replay-lpt-at (previous step)

lpt[n0] = mklp(m3, m4, lpf0, m5), n0 < # lpt ⊦ (lpf0 = LP_FREE ∨ n0 ∈ nx ⊃ replay-lpt(lpt, nx, n0) ;(lpf0 = LP_INDEX_NODES ∧ m3 ≠ 0 ⊃ replay-lpt(lpt, nx, n0)[n0, mklp(m3, LEB_SIZE, LP_INDEX_NODES, m5)] ;(m3 = 0 ⊃ replay-lpt(lpt, nx, n0)[n0, mklp(0, 0, LP_FREE, m5)];replay-lpt(lpt, nx, n0)) ) ) [n0 ] = (lpf0 = LP_FREE ∨ n0 ∈ nx ⊃ mklp(m3, m4, lpf0, m5) ;(lpf0 = LP_INDEX_NODES ∧ m3 ≠ 0 ⊃ mklp(m3, LEB_SIZE, LP_INDEX_NODES, m5);(m3 = 0 ⊃ mklp(0, 0, LP_FREE, m5);mklp(m3, m4, lpf0, m5))) )

User applied rule case distinction

And obtained the following new goals

Proof step 13:
lpt[n0] = mklp(m3, m4, lpf0, m5), n0 < # lpt ⊦ (lpf0 = LP_INDEX_NODES ∧ m3 ≠ 0 ⊃ replay-lpt(lpt, nx, n0)[n0, mklp(m3, LEB_SIZE, LP_INDEX_NODES, m5)] ;(m3 = 0 ⊃ replay-lpt(lpt, nx, n0)[n0, mklp(0, 0, LP_FREE, m5)];replay-lpt(lpt, nx, n0)) ) [n0 ] = (lpf0 = LP_FREE ∨ n0 ∈ nx ⊃ mklp(m3, m4, lpf0, m5) ;(lpf0 = LP_INDEX_NODES ∧ m3 ≠ 0 ⊃ mklp(m3, LEB_SIZE, LP_INDEX_NODES, m5);(m3 = 0 ⊃ mklp(0, 0, LP_FREE, m5);mklp(m3, m4, lpf0, m5))) ), lpf0 = LP_FREE, n0 ∈ nx

Rule argument

pos: right 1

Additional information

Used simplifier rules: replay-lpt-at-above: n ≤ m, m < # lpt ⊦ replay-lpt(lpt, nx, n)[m] = lpt[m];% ⊦ m ≤ m; (s)