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Proof step 30 from proof abs-gstore-cleanup-lpt (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 31:
⊦ n ∈ ns ∩ ns0 ↔ n ∈ ns ∧ n ∈ ns0
Proof step 32:
# lpt = # avol1, # avol0 = # avol1, lpt[n] = mklp(m3, m1, LP_GROUP_NODES, m2), gstore[n] = groupblock(gndx0, lax0, m3), n < # avol1, n ∈ gstore, ¬ n ∈ ginval → abs-leb(avol0[n], groupblock(gndx0, lax0, m3), mklp(m3, m1, LP_GROUP_NODES, m2)), ∀ n. n < # avol1 ∧ (lpt[n].ref-size ≠ 0 ∨ lpt[n].flags = LP_FREE) → avol0[n] = avol1[n] ⊦ m3 = 0, abs-leb(avol1[n], groupblock(gndx0, lax0, m3), mklp(m3, m1, LP_GROUP_NODES, m2)), n ∈ dom remove-refsize0(gstore) ∧ n ∈ ginval

Rule argument

spec: set-union, inst: nat-set name: Intersect seq: ⊦ n ∈ ns ∩ ns0 ↔ n ∈ ns ∧ n ∈ ns0 subst: [ns0, ns, n] → [ginval, dom remove-refsize0(gstore), n] flags: <all paths>

Additional information

Used terms: ginval, dom remove-refsize0(gstore), n