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Proof step 21 from proof abs-gstore-cleanup-lpt (previous step)

# lpt = # avol1, # avol0 = # avol1, lpf = LP_GROUP_NODES ↔ n ∈ gstore, remove-refsize0(gstore)[n] = groupblock(gndx, lax, m), gstore[n] = groupblock(gndx0, lax0, m3), lpt[n] = mklp(m0, m1, lpf, m2), dom remove-refsize0(gstore) ∩ ginval = ∅, n < # avol1, n ∈ gstore → m0 = m3, n ∈ gstore ∧ ¬ n ∈ ginval → abs-leb(avol0[n], groupblock(gndx0, lax0, m3), mklp(m0, m1, lpf, m2)), ∀ n. n < # avol1 ∧ (lpt[n].ref-size ≠ 0 ∨ lpt[n].flags = LP_FREE) → avol0[n] = avol1[n], ¬(n ∈ gstore ↔ n ∈ remove-refsize0(gstore)) ∨ ¬(n ∈ remove-refsize0(gstore) → abs-leb(avol1[n], groupblock(gndx, lax, m), mklp(m0, m1, lpf, m2))) ∨ ¬(n ∈ remove-refsize0(gstore) → m0 = m) ⊦ lpf = LP_FREE, m0 = 0

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 22:
# avol0 = # avol1, # lpt = # avol1, lpf = LP_GROUP_NODES ↔ n ∈ gstore, lpt[n] = mklp(m0, m1, lpf, m2), gstore[n] = groupblock(gndx0, lax0, m3), remove-refsize0(gstore)[n] = groupblock(gndx, lax, m), lpf = LP_GROUP_NODES, dom remove-refsize0(gstore) ∩ ginval = ∅, n < # avol1, n ∈ gstore ∧ ¬ n ∈ ginval → abs-leb(avol0[n], groupblock(gndx0, lax0, m3), mklp(m0, m1, lpf, m2)), n ∈ gstore → m0 = m3, ∀ n. n < # avol1 ∧ (lpt[n].ref-size ≠ 0 ∨ lpt[n].flags = LP_FREE) → avol0[n] = avol1[n], ¬(n ∈ gstore ↔ n ∈ remove-refsize0(gstore)) ∨ ¬(n ∈ remove-refsize0(gstore) → abs-leb(avol1[n], groupblock(gndx, lax, m), mklp(m0, m1, lpf, m2))) ∨ ¬(n ∈ remove-refsize0(gstore) → m0 = m) ⊦ lpf = LP_FREE, m0 = 0

Rule argument

fma: lpf = LP_GROUP_NODES

Additional information

Used simplifier rules: ⊦ ¬ n ∈ gstore → gstore[n] = (∅)[n]; (s)% ⊦ n ∈ remove-refsize0(gstore) ↔ n ∈ gstore ∧ gstore[n].ref-size ≠ 0; (ws) Used formulas: lpf = LP_GROUP_NODES