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Proof step 5 from proof union-keys (conclusion)

⊦ (st ∪ st0) .keys = st .keys ∪ st0 .keys

User applied rule structural induction

And obtained the following new goals

Proof step 1:
⊦ st ∪ ∅ = st
Proof step 4:
∀ st. (st ∪ st1) .keys = st .keys ∪ st1 .keys ⊦ (st ∪ st1[rk, val]) .keys = st .keys ∪ st1[rk, val] .keys

Rule argument

[VARWITHVARSEQSARG : st0, ()]

Additional information

[[CONCRETESIMPRULES : ([CSIMPGEN : store generated by ∅, [];], [CSIMPSEQ : ⊦ ∅ .keys = ∅], [CSIMPSEQ : ⊦ rks ∪ ∅ = rks], [CSIMPSEQ : ⊦ (rks ∪ rks0) ∪ rks1 = rks ∪ rks0 ∪ rks1], [CSIMPSEQ : ⊦ rks ∪ rks0 = rks0 ∪ rks])]]