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Proof step 10 from proof unmodified-clean-eq-adr-subseteq (previous step)

# zbrar0 = BRANCH_SIZE, BRANCH_SIZE = # zbrar1, iast1[adr] = indexnode(save(zbrar0, 0, nused), bv, nused), iast0[adr] = indexnode(save(zbrar0, 0, nused), bv, nused), zbrar1[n] = mkzbranch(key1, adr1, r1), zbrar0[n] = mkzbranch(key0, adr0, r0), indexnode(save(zbrar0, 0, nused), bv, nused) = save(mkznode(rp1, zbrar1, bv, false, nused)), n < nused, n < BRANCH_SIZE, adr ∈ iast1, adr ∈ iast0, nused ≤ BRANCH_SIZE ⊦ key1 = key0 ∧ adr1 = adr0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ save(znd) = indexnode(save(znd.zbranches, 0, znd.usedsize), znd.leaf, znd.usedsize)
Proof step 12:
# zbrar0 = BRANCH_SIZE, BRANCH_SIZE = # zbrar1, zbrar0[n] = mkzbranch(key0, adr0, r0), zbrar1[n] = mkzbranch(key1, adr1, r1), iast0[adr] = indexnode(save(zbrar0, 0, nused), bv, nused), iast1[adr] = indexnode(save(zbrar0, 0, nused), bv, nused), indexnode(save(zbrar0, 0, nused), bv, nused) = indexnode (save(mkznode(rp1, zbrar1, bv, false, nused).zbranches, 0, mkznode(rp1, zbrar1, bv, false, nused).usedsize), mkznode(rp1, zbrar1, bv, false, nused).leaf, mkznode(rp1, zbrar1, bv, false, nused).usedsize), n < BRANCH_SIZE, n < nused, adr ∈ iast0, adr ∈ iast1, nused ≤ BRANCH_SIZE ⊦ key1 = key0 ∧ adr1 = adr0

Rule argument

spec: znode-ops name: save-node seq: ⊦ save(znd) = indexnode (save(znd.zbranches, 0, znd.usedsize), znd.leaf, znd.usedsize) subst: [znd] → [mkznode(rp1, zbrar1, bv, false, nused)] flags: <all paths>

Additional information

Used terms: mkznode(rp1, zbrar1, bv, false, nused)