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Proof step 5 from proof abs-gstore-set-refsize (previous step)

gstore[n, groupblock(gndx, lax, m0)][n5] = groupblock(gndx0, lax0, m), lpt[n] = mklp(n0, n1, LP_GROUP_NODES, n4), gstore[n] = groupblock(gndx, lax, n3), n ∈ gstore, ∀ n. (n < # lpt ∧ lpt[n].flags = LP_GROUP_NODES ↔ n ∈ gstore) ∧ (n ∈ gstore ∧ ¬ n ∈ ginval → abs-leb(avol[n], gstore[n], lpt[n])) ∧ (n ∈ gstore → lpt[n].ref-size = gstore[n].ref-size) ⊦ (n5 < # lpt ∧ lpt[n, mklp(m0, n1, LP_GROUP_NODES, n2)][n5].flags = LP_GROUP_NODES ↔ n5 ∈ gstore[n, groupblock(gndx, lax, m0)]) ∧ ( n5 ∈ gstore[n, groupblock(gndx, lax, m0)] ∧ ¬ n5 ∈ ginval → abs-leb(avol[n5], groupblock(gndx0, lax0, m), lpt[n, mklp(m0, n1, LP_GROUP_NODES, n2)][n5])) ∧ (n5 ∈ gstore[n, groupblock(gndx, lax, m0)] → lpt[n, mklp(m0, n1, LP_GROUP_NODES, n2)][n5].ref-size = m)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 6:
gstore[n] = groupblock(gndx, lax, n3), lpt[n] = mklp(n0, n1, LP_GROUP_NODES, n4), gstore[n, groupblock(gndx, lax, m0)][n5] = groupblock(gndx0, lax0, m), lpt[n, mklp(m0, n1, LP_GROUP_NODES, n2)][n5] = mklp(m1, m2, lpf, m3), n ∈ gstore, ∀ n. (n < # lpt ∧ lpt[n].flags = LP_GROUP_NODES ↔ n ∈ gstore) ∧ (n ∈ gstore ∧ ¬ n ∈ ginval → abs-leb(avol[n], gstore[n], lpt[n])) ∧ (n ∈ gstore → lpt[n].ref-size = gstore[n].ref-size) ⊦ (n5 < # lpt ∧ lpf = LP_GROUP_NODES ↔ n5 ∈ gstore[n, groupblock(gndx, lax, m0)]) ∧ ( n5 ∈ gstore[n, groupblock(gndx, lax, m0)] ∧ ¬ n5 ∈ ginval → abs-leb(avol[n5], groupblock(gndx0, lax0, m), lpt[n, mklp(m0, n1, LP_GROUP_NODES, n2)][n5])) ∧ (n5 ∈ gstore[n, groupblock(gndx, lax, m0)] → m1 = 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[n, mklp(m0, n1, LP_GROUP_NODES, n2)][n5], m1, m2, lpf, m3]

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[n, mklp(m0, n1, LP_GROUP_NODES, n2)][n5], m1, m2, lpf, m3