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Proof step 19 from proof save-same-payload-same (previous step)

# zbrar1 = BRANCH_SIZE, # zbrar0 = BRANCH_SIZE, payload(zbrar1, n, m0) = payload(zbrar0, n, m0), save(zbrar1, n, m0) = save(zbrar0, n, m0), save(zbrar0[n + m0]) = save(zbrar1[n + m0]), n + m0 < BRANCH_SIZE ⊦ payload(zbrar0, n, m0) ⊕ (zbrar0[n + m0].entry? ⊃ (∅)[zbrar0[n + m0].key, zbrar0[n + m0].adr];∅) = payload(zbrar0, n, m0) ⊕ (zbrar1[n + m0].entry? ⊃ (∅)[zbrar1[n + m0].key, zbrar1[n + m0].adr];∅)

User applied rule structural induction

And obtained the following new goals

Proof step 20:
# zbrar0 = BRANCH_SIZE, # zbrar1 = BRANCH_SIZE, mkzbranch(key', adr, rp) = zbrar0[n + m0], payload(zbrar1, n, m0) = payload(zbrar0, n, m0), save(zbrar0[n + m0]) = save(zbrar1[n + m0]), save(zbrar1, n, m0) = save(zbrar0, n, m0), n + m0 < BRANCH_SIZE ⊦ payload(zbrar0, n, m0) ⊕ (zbrar0[n + m0].entry? ⊃ (∅)[zbrar0[n + m0].key, zbrar0[n + m0].adr];∅) = payload(zbrar0, n, m0) ⊕ (zbrar1[n + m0].entry? ⊃ (∅)[zbrar1[n + m0].key, zbrar1[n + m0].adr];∅)
Proof step 23:
# zbrar0 = BRANCH_SIZE, # zbrar1 = BRANCH_SIZE, mkzentry(key', adr) = zbrar0[n + m0], payload(zbrar1, n, m0) = payload(zbrar0, n, m0), save(zbrar0[n + m0]) = save(zbrar1[n + m0]), save(zbrar1, n, m0) = save(zbrar0, n, m0), n + m0 < BRANCH_SIZE ⊦ payload(zbrar0, n, m0) ⊕ (zbrar0[n + m0].entry? ⊃ (∅)[zbrar0[n + m0].key, zbrar0[n + m0].adr];∅) = payload(zbrar0, n, m0) ⊕ (zbrar1[n + m0].entry? ⊃ (∅)[zbrar1[n + m0].key, zbrar1[n + m0].adr];∅)

Rule argument

term: zbrar0[n + m0]

Additional information

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