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Proof step 7 from proof at-put-keys-01 (previous step)

⊦ sk = sk0, (st[r -- (sks + sk '), val][r0 -- sk0]) = st[r0 -- sk0]

User applied rule structural induction

And obtained the following new goals

Proof step 1:
⊦ st[r -- sk ', val] = st[r -- sk, val]
Proof step 6:
∀ sk, sk0, st, r, val, r0. sk = sk0 ∨ (st[r -- (sks0 + sk '), val][r0 -- sk0]) = st[r0 -- sk0] ⊦ sk = sk0, (st[r -- ((sk1 + sks0) + sk '), val][r0 -- sk0]) = st[r0 -- sk0]

Rule argument

[VARWITHVARSEQSARG : sks, ()]

Additional information

[[CONCRETESIMPRULES : ([CSIMPGEN : storekeys generated by [], +;], [CSIMPSEQ : ⊦ [] + sks = sks], [CSIMPSEQ : ⊦ (sks + sks0) + sks1 = sks + sks0 + sks1], [CSIMPSEQ : ⊦ sk ≠ sk0 → (st[r -- sk, val][r0 -- sk0]) = st[r0 -- sk0]])]]