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Proof step 5 from proof fwd-in-gstore-lpt (previous step)

gstore[n] = groupblock(gndx, lax, m), lpt[n] = mklp(m0, m1, lpf, m2), abs-gstore(avol, lpt, gstore, ginval), n ∈ gstore ⊦ n < # lpt ∧ m0 = m ∧ lpf = LP_GROUP_NODES

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ abs-gstore(avol, lpt, gstore, ginval) ↔ (∀ 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))
Proof step 7:
lpt[n] = mklp(m0, m1, lpf, m2), gstore[n] = groupblock(gndx, lax, m), 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) ⊦ n < # lpt ∧ m0 = m ∧ lpf = LP_GROUP_NODES

Rule argument

spec: persistence-base name: abs-gstore-def seq: ⊦ abs-gstore(avol, lpt, gstore, ginval) ↔ (∀ 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)) subst: [ginval, gstore, lpt, avol] → [ginval, gstore, lpt, avol] flags: <all paths>

Additional information

Used terms: ginval, gstore, lpt, avol