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Proof step 85 from proof union-addarray-rew (previous step)

newref(r, st), newref(r, st0) ⊦ addarray(r, ty, vals, st ∪ st0) = st ∪ addarray(r, ty, vals, st0), r = jvmref

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 1:
⊦ st1 = st2 ↔ (∀ rk. (rk ∈ st1 ↔ rk ∈ st2) ∧ st1[rk] = st2[rk])
Proof step 84:
newref(r, st), newref(r, st0) ⊦ ∀ rk. (rk ∈ addarray(r, ty, vals, st ∪ st0) ↔ rk ∈ st ∪ addarray(r, ty, vals, st0)) ∧ (addarray(r, ty, vals, st ∪ st0)[rk]) = (st ∪ addarray(r, ty, vals, st0))[rk], r = jvmref

Rule argument

[speclemmaarg: ,st1 = st2 ↔ (∀ rk. (rk ∈ st1 ↔ rk ∈ st2) ∧ st1[rk] = st2[rk]) ,[st2, st1] → [st ∪ addarray(r, ty, vals, st0), addarray(r, ty, vals, st ∪ st0)] ,F ,store ,javastore ,Extension ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st ∪ addarray(r, ty, vals, st0), addarray(r, ty, vals, st ∪ st0))]]