1. a : LOSet
2. b : AbDMon
3. k : |a|
⊢ inj(k,e) = 00 ∈ |oal(a;b)|
{ ((BLemma `lookups_same_a` THENM D 0) THENA Auto) }
4. u : |a|
⊢ (inj(k,e)[u]) = (00[u]) ∈ |b|