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Proof step 8 from proof lookup-put-rkvs (previous step)

∀ rk, rk0, st, val. rk = rk0 ∨ (st[rk, val][rkvs0][rk0]) = (st[rkvs0][rk0]) ⊦ rk = rk0, (st[rk, val][rk1, val0][rkvs0][rk0]) = (st[rk1, val0][rkvs0][rk0])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ rk ≠ rk0 → (st[rk0, val][rk, val0]) = (st[rk, val0][rk0, val])
Proof step 7:
rk1 ≠ rk, ∀ rk, rk0, st, val. rk = rk0 ∨ (st[rk, val][rkvs0][rk0]) = (st[rkvs0][rk0]) ⊦ rk = rk0, (st[rk1, val0][rk, val][rkvs0][rk0]) = (st[rk1, val0][rkvs0][rk0])

Rule argument

[speclemmaarg: ,rk ≠ rk0 → (st[rk0, val][rk, val0]) = (st[rk, val0][rk0, val]) ,[val0, rk, val, rk0, st] → [val0, rk1, val, rk, st] ,F ,store ,javastore-ostorea ,rew ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (st[rk, val][rk, val0]) = st[rk, val0]])], [EXTRATERMS : (val0, rk1, val, rk, st)]]