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Proof step 19 from proof union-addarray-rew (previous step)

newref(r0, st), newref(r0, st0) ⊦ r0 = jvmref, (r0 -- fs ' ∈ addarray(r0, ty, vals, st ∪ st0) ↔ r0 -- fs ' ∈ st ∨ r0 -- fs ' ∈ addarray(r0, ty, vals, st0)) ∧ (addarray(r0, ty, vals, st ∪ st0)[r0 -- fs ']) = (st ∪ addarray(r0, ty, vals, st0))[r0 -- fs '], fs ' ≠ _type ∧ fs ' ≠ _length

User applied rule case distinction

And obtained the following new goals

Proof step 11:
newref(r0, st), newref(r0, st0) ⊦ fs ' ≠ _type, r0 = jvmref, (r0 -- fs ' ∈ addarray(r0, ty, vals, st ∪ st0) ↔ r0 -- fs ' ∈ st ∨ r0 -- fs ' ∈ addarray(r0, ty, vals, st0)) ∧ (addarray(r0, ty, vals, st ∪ st0)[r0 -- fs ']) = (st ∪ addarray(r0, ty, vals, st0))[r0 -- fs ']
Proof step 18:
newref(r0, st), newref(r0, st0) ⊦ fs ' ≠ _length, r0 = jvmref, (r0 -- fs ' ∈ addarray(r0, ty, vals, st ∪ st0) ↔ r0 -- fs ' ∈ st ∨ r0 -- fs ' ∈ addarray(r0, ty, vals, st0)) ∧ (addarray(r0, ty, vals, st ∪ st0)[r0 -- fs ']) = (st ∪ addarray(r0, ty, vals, st0))[r0 -- fs ']

Rule argument

[CASEDARG : pos: right 3, ()]

Additional information

[[CONCRETESIMPRULES : ()]]