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Proof step 8 from proof hasKeys-app (conclusion)

⊦ hasKeys(r, sks + sks0, st) ↔ hasKeys(r, sks, st) ∧ hasKeys(r, sks0, st)

User applied rule structural induction

And obtained the following new goals

Proof step 1:
⊦ hasKeys(r, [], st)
Proof step 7:
∀ r, sks0, st. hasKeys(r, sks1 + sks0, st) ↔ hasKeys(r, sks1, st) ∧ hasKeys(r, sks0, st) ⊦ hasKeys(r, (sk + sks1) + sks0, st) ↔ hasKeys(r, sk + sks1, st) ∧ hasKeys(r, sks0, st)

Rule argument

[VARWITHVARSEQSARG : sks, ()]

Additional information

[[CONCRETESIMPRULES : ([CSIMPGEN : storekeys generated by [], +;], [CSIMPSEQ : ⊦ [] + sks = sks], [CSIMPSEQ : ⊦ (sks + sks0) + sks1 = sks + sks0 + sks1])]]