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Proof step 9 from proof validrefkeynotnull-addarray (previous step)

st[rk] = refval(r), newref(r1, st), rk ∈ st, validrefnotnull(str, r, ty1, st) ⊦ r1 = jvmref, is_referencevalue(addarray(r1, ty, vals, st)[rk]) ∧ validrefnotnull(str, (addarray(r1, ty, vals, st)[rk]) .refval, ty1, addarray(r1, ty, vals, st))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ rk .ref ≠ r → (addarray(r, ty, vals, st)[rk]) = st[rk]
Proof step 7:
¬ rk .ref ≠ r1, st[rk] = refval(r), newref(r1, st), rk ∈ st, validrefnotnull(str, r, ty1, st) ⊦ r1 = jvmref, is_referencevalue(addarray(r1, ty, vals, st)[rk]) ∧ validrefnotnull(str, (addarray(r1, ty, vals, st)[rk]) .refval, ty1, addarray(r1, ty, vals, st))
Proof step 8:
⊦ newref(r1, st) ∧ validrefnotnull(str, r, ty1, st) → validrefnotnull(str, r, ty1, addarray(r1, ty, vals, st))

Rule argument

[speclemmaarg: ,rk .ref ≠ r → (addarray(r, ty, vals, st)[rk]) = st[rk] ,[rk, st, vals, ty, r] → [rk, st, vals, ty, r1] ,F ,addarray , ,add-at-01 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ is_referencevalue(refval(r))], [CSIMPSEQ : ⊦ refval(r) .refval = r])], [EXTRATERMS : (rk, st, vals, ty, r1)]]