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Proof step 80 from proof union-addarray-rew (previous step)

newref(r, st), newref(r, st0) ⊦ r = jvmref, r = r0, (st ∪ st0)[r0 -- sk] = (st ∪ addarray(r, ty, vals, st0))[r0 -- sk]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 76:
⊦ ¬ rk ∈ st0 → (st ∪ st0)[rk] = st[rk]
Proof step 77:
⊦ r ≠ r0 → (addarray(r, ty, vals, st)[r0 -- sk]) = st[r0 -- sk]
Proof step 78:
⊦ r ≠ r0 → (r -- sk ∈ addarray(r0, ty, vals, st) ↔ r -- sk ∈ st)
Proof step 79:
⊦ r ≠ r0 → (r -- sk ∈ addarray(r0, ty, vals, st) ↔ r -- sk ∈ st)

Rule argument

[speclemmaarg: ,¬ rk ∈ st0 → (st ∪ st0)[rk] = st[rk] ,[rk, st0, st] → [r0 -- sk, addarray(r, ty, vals, st0), st] ,F ,storefunsx , ,union-at-left ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ rk ∈ st0 → (st ∪ st0)[rk] = st0[rk]], [CSIMPSEQ : ⊦ ¬ rk ∈ st0 → (st ∪ st0)[rk] = st[rk]])], [EXTRATERMS : (r0 -- sk, addarray(r, ty, vals, st0), st)]]