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Proof step 29 from proof validrefkeynotnull-union (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ validrefkeynotnull(str, rk, ty, st) ↔ rk ∈ st ∧ validrefvalnotnull(str, st[rk], ty, st)
Proof step 28:
validrefvalnotnull(str, st[rk], ty, st), rk ∈ st ⊦ rk ∈ st0 ∪ st ∧ validrefvalnotnull(str, (st0 ∪ st)[rk], ty, st0 ∪ st)

Rule argument

[crewrite-arg: validrefkeynotnull-def , F , [st, ty, rk, str] → [st0 ∪ st, ty, rk, str] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st0 ∪ st, ty, rk, str)]]