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Proof step 28 from proof validrefkeynotnull-union (previous step)

validrefvalnotnull(str, st[rk], ty, st), rk ∈ st ⊦ rk ∈ st0 ∪ st ∧ validrefvalnotnull(str, (st0 ∪ st)[rk], ty, st0 ∪ st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ validrefvalnotnull(str, val, ty, st) ↔ is_referencevalue(val) ∧ validrefnotnull(str, val .refval, ty, st)
Proof step 27:
is_referencevalue(st[rk]) ∧ validrefnotnull(str, st[rk] .refval, ty, st), rk ∈ st ⊦ rk ∈ st0 ∪ st ∧ validrefvalnotnull(str, (st0 ∪ st)[rk], ty, st0 ∪ st)

Rule argument

[crewrite-arg: validrefvalnotnull-def , F , [st, ty, val, str] → [st, ty, st[rk], str] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, ty, st[rk], str)]]