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Proof step 83 from proof union-addarray-rew (previous step)

newref(r, st), newref(r, st0) ⊦ r = jvmref, (rk ∈ addarray(r, ty, vals, st ∪ st0) ↔ rk ∈ st ∨ rk ∈ addarray(r, ty, vals, st0)) ∧ (addarray(r, ty, vals, st ∪ st0)[rk]) = (st ∪ addarray(r, ty, vals, st0))[rk]

User applied rule structural induction

And obtained the following new goals

Proof step 82:
newref(r, st), newref(r, st0) ⊦ r = jvmref, (r0 -- sk ∈ addarray(r, ty, vals, st ∪ st0) ↔ r0 -- sk ∈ st ∨ r0 -- sk ∈ addarray(r, ty, vals, st0)) ∧ (addarray(r, ty, vals, st ∪ st0)[r0 -- sk]) = (st ∪ addarray(r, ty, vals, st0))[r0 -- sk]

Rule argument

[VARWITHVARSEQSARG : rk, ()]

Additional information

[[CONCRETESIMPRULES : ([CSIMPGEN : refkey generated by --;])]]