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Proof step 8 from proof hasKeys-put-01 (previous step)

rk ∈ st, ∀ rk, st, r, val. rk ∈ st → (hasKeys(r, sks0, st[rk, val]) ↔ hasKeys(r, sks0, st)) ⊦ r -- sk ∈ st[rk, val] ∧ hasKeys(r, sks0, st[rk, val]) ↔ r -- sk ∈ st ∧ hasKeys(r, sks0, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ rk ∈ st[rk0, val] ↔ rk = rk0 ∨ rk ∈ st
Proof step 7:
rk ∈ st, ∀ rk, st, r, val. rk ∈ st → (hasKeys(r, sks0, st[rk, val]) ↔ hasKeys(r, sks0, st)) ⊦ (r -- sk = rk ∨ r -- sk ∈ st) ∧ hasKeys(r, sks0, st[rk, val]) ↔ r -- sk ∈ st ∧ hasKeys(r, sks0, st)

Rule argument

[speclemmaarg: ,rk ∈ st[rk0, val] ↔ rk = rk0 ∨ rk ∈ st ,[val, rk0, st, rk] → [val, rk, st, r -- sk] ,F ,store ,javastore-ostorea ,In-insert ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (val, rk, st, r -- sk)]]