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Proof step 2 from proof validrefkeynotnull-union-same (previous step)

validrefkeynotnull(str, r -- fs ', ty, st1) ⊦ st1[r -- fs '] = (st ∪ st1)[r -- fs ']

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 1:
⊦ validrefkeynotnull(str, rk, ty, st) ↔ rk ∈ st ∧ validrefvalnotnull(str, st[rk], ty, st)

Rule argument

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

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ rk ∈ st0 → (st ∪ st0)[rk] = st0[rk]])], [EXTRATERMS : (st1, ty, r -- fs ', str)]]