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Proof step 31 from proof validrefkeynotnull-subset (previous step)

validrefvalnotnull(str, st[rk], ty, st), rk ∈ st, st ⊆ st1 ⊦ validrefkeynotnull(str, rk, ty, st1)

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 30:
validrefvalnotnull(str, st[rk], ty, st), rk ∈ st, st ⊆ st1 ⊦ rk ∈ st1 ∧ validrefvalnotnull(str, st1[rk], ty, st1)

Rule argument

[crewrite-arg: validrefkeynotnull-def , F , [st, ty, rk, str] → [st1, ty, rk, str] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st1, ty, rk, str)]]