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Proof step 22 from proof unmodified-clean-eq-keys-subseteq (previous step)

# 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]) = mkentry(key', adr0), n < BRANCH_SIZE, n < nused, adr ∈ iast0, adr ∈ iast1, nused ≤ BRANCH_SIZE ⊦ zbrar1[n].key = key'

User applied rule structural induction

And closed the goal!

Rule argument

term: zbrar1[n]

Additional information

Used simplifier rules: zbranch freely generated by mkzbranch, mkzentry;;% ⊦ save(mkzentry(key, adr)) = mkentry(key, adr); (s)% ⊦ mkentry(key, adr) = mkentry(key0, adr0) ↔ key = key0 ∧ adr = adr0; (ws)% ⊦ mkzentry(key, adr).key = key; (s)% ⊦ save(mkzbranch(key, adr, r)) = mkbranch(key, adr); (s)% ⊦ mkbranch(key, adr) ≠ mkentry(key0, adr0); (s)