[Imprint][Data Privacy Statement][E-Mail]

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Proof step 5 from proof abs-gstore-reduce-write (previous step)

# lpt = # avol, ∀ n. (n < # avol ∧ 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) ⊦ (∀ n0. (n0 < # avol ∧ lpt[n, lp][n0].flags = LP_GROUP_NODES ↔ n0 ∈ gstore[n, groupblock(gndx, lax, m)]) ∧ ( n0 ∈ gstore[n, groupblock(gndx, lax, m)] ∧ ¬ n0 ∈ ginval → abs-leb(avol[n, aleb][n0], gstore[n, groupblock(gndx, lax, m)][n0], lpt[n, lp][n0])) ∧ (n0 ∈ gstore[n, groupblock(gndx, lax, m)] → lpt[n, lp][n0].ref-size = gstore[n, groupblock(gndx, lax, m)][n0].ref-size)) ↔ n < # avol ∧ ((lpt[n].flags = LP_GROUP_NODES → lpt[n].ref-size = gstore[n].ref-size) → lp.ref-size = m ∧ lp.flags = LP_GROUP_NODES) ∧ (¬ n ∈ ginval ∧ (lpt[n].flags = LP_GROUP_NODES → abs-leb(avol[n], gstore[n], lpt[n])) → abs-leb(aleb, groupblock(gndx, lax, m), lp))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

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

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] → [lp, m0, m1, lpf, m2]

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: lp, m0, m1, lpf, m2