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Proof step 7 from proof in-put-keys (previous step)

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

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, r0, st, r, val. sk = sk0 ∨ (r0 -- sk0 ∈ st[r -- (sks0 + sk '), val] ↔ r0 -- sk0 ∈ st) ⊦ sk = sk0, r0 -- sk0 ∈ st[r -- ((sk1 + sks0) + sk '), val] ↔ r0 -- sk0 ∈ st

Rule argument

[VARWITHVARSEQSARG : sks, ()]

Additional information

[[CONCRETESIMPRULES : ([CSIMPGEN : storekeys generated by [], +;], [CSIMPSEQ : ⊦ [] + sks = sks], [CSIMPSEQ : ⊦ (sks + sks0) + sks1 = sks + sks0 + sks1], [CSIMPSEQ : ⊦ rk ∈ st[rk0, val] ↔ rk = rk0 ∨ rk ∈ st], [CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ r = r0 ∧ sk = sk0], [CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ ¬ ¬ (r = r0 ∧ sk = sk0)])]]