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Proof step 5 from proof abs-gstore-idcircle (previous step)

# lpt = # avol1, # avol0 = # avol1, gstore[n0] = groupblock(gndx, lax, m), lpt[n] = mklp(m0, m1, lpf, m2), n < # avol1, id○(avol0, avol1, n), ∀ n. (n < # avol1 ∧ lpt[n].flags = LP_GROUP_NODES ↔ n ∈ gstore) ∧ (n ∈ gstore ∧ ¬ n ∈ ginval → abs-leb(avol0[n], gstore[n], lpt[n])) ∧ (n ∈ gstore → lpt[n].ref-size = gstore[n].ref-size) ⊦ lpf = LP_GROUP_NODES, (n0 < # avol1 ∧ lpt[n0].flags = LP_GROUP_NODES ↔ n0 ∈ gstore) ∧ (n0 ∈ gstore ∧ ¬ n0 ∈ ginval → abs-leb(avol1[n0], groupblock(gndx, lax, m), lpt[n0])) ∧ (n0 ∈ gstore → lpt[n0].ref-size = m)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 6:
# avol0 = # avol1, # lpt = # avol1, lpt[n] = mklp(m0, m1, lpf, m2), gstore[n0] = groupblock(gndx, lax, m), lpt[n0] = mklp(m3, m4, lpf0, m5), n < # avol1, id○(avol0, avol1, n), ∀ n. (n < # avol1 ∧ lpt[n].flags = LP_GROUP_NODES ↔ n ∈ gstore) ∧ (n ∈ gstore ∧ ¬ n ∈ ginval → abs-leb(avol0[n], gstore[n], lpt[n])) ∧ (n ∈ gstore → lpt[n].ref-size = gstore[n].ref-size) ⊦ lpf = LP_GROUP_NODES, (n0 < # avol1 ∧ lpf0 = LP_GROUP_NODES ↔ n0 ∈ gstore) ∧ (n0 ∈ gstore ∧ ¬ n0 ∈ ginval → abs-leb(avol1[n0], groupblock(gndx, lax, m), lpt[n0])) ∧ (n0 ∈ gstore → m3 = m)

Rule argument

spec: lprops name: elim seq: ⊦ ((m = lp.ref-size ∧ m0 = lp.size) ∧ lpf = lp.flags) ∧ m1 = lp.gcheapidx ↔ lp = mklp(m, m0, lpf, m1) subst: [lp, m, m0, lpf, m1] → [lpt[n0], m3, m4, lpf0, m5]

Additional information

Used simplifier rules: ⊦ ((m = lp.ref-size ∧ m0 = lp.size) ∧ lpf = lp.flags) ∧ m1 = lp.gcheapidx ↔ lp = mklp(m, m0, lpf, m1); (elim) Used terms: lpt[n0], m3, m4, lpf0, m5