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Proof step 9 from proof unmodified-clean-fwd-zbrar (previous step)

# zbrar0 = BRANCH_SIZE, BRANCH_SIZE = # zbrar1, iast[adr] = indexnode(save(zbrar0, 0, nused), bv, nused), zbrar0[n] = mkzbranch(key, adr0, r2), save(zbrar1, 0, nused) = save(zbrar0, 0, nused), n < BRANCH_SIZE, n < nused, adr ∈ iast, nused ≤ BRANCH_SIZE ⊦ ∃ r0. zbrar1[n] = mkzbranch(key, adr0, r0)

User applied rule structural induction

And obtained the following new goals

Proof step 10:
# zbrar0 = BRANCH_SIZE, BRANCH_SIZE = # zbrar1, zbrar0[n] = mkzbranch(key, adr0, r2), iast[adr] = indexnode(save(zbrar0, 0, nused), bv, nused), mkzbranch(key', adr1, rp) = zbrar1[n], save(zbrar1, 0, nused) = save(zbrar0, 0, nused), n < nused, n < BRANCH_SIZE, adr ∈ iast, nused ≤ BRANCH_SIZE ⊦ ∃ r0. zbrar1[n] = mkzbranch(key, adr0, r0)
Proof step 15:
# zbrar0 = BRANCH_SIZE, BRANCH_SIZE = # zbrar1, zbrar0[n] = mkzbranch(key, adr0, r2), iast[adr] = indexnode(save(zbrar0, 0, nused), bv, nused), mkzentry(key', adr1) = zbrar1[n], save(zbrar1, 0, nused) = save(zbrar0, 0, nused), n < nused, n < BRANCH_SIZE, adr ∈ iast, nused ≤ BRANCH_SIZE ⊦ ∃ r0. zbrar1[n] = mkzbranch(key, adr0, r0)

Rule argument

term: zbrar1[n]

Additional information

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