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Proof step 18 from proof unmodified-clean-eq-keys-subseteq (previous step)

# zbrar0 = BRANCH_SIZE, BRANCH_SIZE = # zbrar1, iast1[adr] = indexnode(save(zbrar1, 0, nused), bv, nused), iast0[adr] = indexnode(save(zbrar1, 0, nused), bv, nused), save(zbrar1[n]) = save(zbrar0[n]), n < nused, n < BRANCH_SIZE, adr ∈ iast1, adr ∈ iast0, nused ≤ BRANCH_SIZE ⊦ zbrar1[n].key = zbrar0[n].key

User applied rule structural induction

And obtained the following new goals

Proof step 19:
# zbrar0 = BRANCH_SIZE, BRANCH_SIZE = # zbrar1, iast0[adr] = indexnode(save(zbrar1, 0, nused), bv, nused), iast1[adr] = indexnode(save(zbrar1, 0, nused), bv, nused), mkzbranch(key', adr0, rp) = zbrar0[n], save(zbrar1[n]) = save(zbrar0[n]), n < BRANCH_SIZE, n < nused, adr ∈ iast0, adr ∈ iast1, nused ≤ BRANCH_SIZE ⊦ zbrar1[n].key = zbrar0[n].key
Proof step 21:
# zbrar0 = BRANCH_SIZE, BRANCH_SIZE = # zbrar1, iast0[adr] = indexnode(save(zbrar1, 0, nused), bv, nused), iast1[adr] = indexnode(save(zbrar1, 0, nused), bv, nused), mkzentry(key', adr0) = zbrar0[n], save(zbrar1[n]) = save(zbrar0[n]), n < BRANCH_SIZE, n < nused, adr ∈ iast0, adr ∈ iast1, nused ≤ BRANCH_SIZE ⊦ zbrar1[n].key = zbrar0[n].key

Rule argument

term: zbrar0[n]

Additional information

Used simplifier rules: zbranch freely generated by mkzbranch, mkzentry;;