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Proof step 4 from proof validrefkeynotnull-union-01 (conclusion)

⊦ validrefkeynotnull(str, rk, ty, st) → validrefkeynotnull(str, rk, ty, st0 ∪ st)

User applied rule insert lemma

And obtained the following new goals

Proof step 1:
⊦ validrefkeynotnull(str, rk, ty, st) ∧ (∃ st0. st1 = st0 ∪ st) → validrefkeynotnull(str, rk, ty, st1)
Proof step 3:
validrefkeynotnull(str, rk, ty, st) ∧ (∃ st2. st0 ∪ st = st2 ∪ st) → validrefkeynotnull(str, rk, ty, st0 ∪ st) ⊦ validrefkeynotnull(str, rk, ty, st) → validrefkeynotnull(str, rk, ty, st0 ∪ st)

Rule argument

[LEMMAARG : validrefkeynotnull-union, [str, rk, ty, st, st1] → [str, rk, ty, st, st0 ∪ st]]

Additional information

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