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Proof step 10 from proof union-addarray-rew (previous step)

fs ' = _type, newref(r0, st0), newref(r0, st) ⊦ r0 = jvmref, typeval(mkarraytype(ty)) = (st ∪ addarray(r0, ty, vals, st0))[r0 -- _type]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ rk ∈ st0 → (st ∪ st0)[rk] = st0[rk]
Proof step 8:
⊦ r -- _type ∈ addarray(r, ty, vals, st)
Proof step 9:
⊦ (addarray(r, ty, vals, st)[r -- _type]) = typeval(mkarraytype(ty))

Rule argument

[speclemmaarg: ,rk ∈ st0 → (st ∪ st0)[rk] = st0[rk] ,[rk, st0, st] → [r0 -- _type, addarray(r0, ty, vals, st0), st] ,F ,storefunsx , ,union-at-right-01 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ rk ∈ st0 → (st ∪ st0)[rk] = st[rk]], [CSIMPSEQ : ⊦ typeval(ty) = typeval(ty0) ↔ ty = ty0])], [EXTRATERMS : (r0 -- _type, addarray(r0, ty, vals, st0), st)]]