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Proof step 51 from proof abs-gstore-replay-lpt-unchanged (previous step)

# lpt = # avol1, # avol0 = # avol1, # gndx = # lax, (lpf0 = LP_FREE ∨ n ∈ 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))) ) = mklp((n ∈ gstore0 ⊃ gstore0[n].ref-size;0), m1, LP_GROUP_NODES, m2), lpt[n] = mklp(m3, m4, lpf0, m5), gstore[n] = groupblock(gndx, lax, m), avol0[n] = mapped(buf), n < # avol1, abs-nodes(buf, gndx, lax, m1 = LEB_SIZE), n ∈ gstore, m1 ≠ LEB_SIZE → m1 = # buf, n ∈ nx ∨ m3 ≠ 0 ∨ lpf0 = LP_FREE → mapped(buf) = avol1[n] ⊦ n ∈ ginval, avol1[n].mapped? ∧ abs-nodes(avol1[n].data, gndx, lax, m1 = LEB_SIZE) ∧ (m1 ≠ LEB_SIZE → m1 = # avol1[n].data)

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 52:
# gndx = # lax, # avol0 = # avol1, # lpt = # avol1, (lpf0 = LP_FREE ∨ n ∈ 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))) ) = mklp((n ∈ gstore0 ⊃ gstore0[n].ref-size;0), m1, LP_GROUP_NODES, m2), avol0[n] = mapped(buf), gstore[n] = groupblock(gndx, lax, m), lpt[n] = mklp(m3, m4, lpf0, m5), n < # avol1, abs-nodes(buf, gndx, lax, m1 = LEB_SIZE), n ∈ gstore, n ∈ nx ∨ m3 ≠ 0 ∨ lpf0 = LP_FREE → mapped(buf) = avol1[n], m1 ≠ LEB_SIZE → m1 = # buf ⊦ lpf0 = LP_FREE, n ∈ ginval, avol1[n].mapped? ∧ abs-nodes(avol1[n].data, gndx, lax, m1 = LEB_SIZE) ∧ (m1 ≠ LEB_SIZE → m1 = # avol1[n].data)

Rule argument

fma: lpf0 = LP_FREE

Additional information

Used simplifier rules: ⊦ mklp(m, m0, lpf, m1) = mklp(m2, m3, lpf0, m4) ↔ m = m2 ∧ m0 = m3 ∧ lpf = lpf0 ∧ m1 = m4; (ws)% ⊦ LP_FREE ≠ LP_GROUP_NODES; (s) Used formulas: lpf0 = LP_FREE