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Proof step 3 from proof validmode-put-nonnull (previous step)

(st[rkvs][_mode]) ≠ noval, st[_mode] = noval ⊦ validmode(str, st[rkvs]) ↔ _mode ∈ st, _mode ∈ rkvs

Heuristic simplifier applied rule simplifier

And closed the goal!

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ∅[rk] = noval], [CSIMPSEQ : ⊦ ¬ rk ∈ st → st[rk] = ∅[rk]], [CSIMPSEQ : ⊦ ¬ rk ∈ rkvs → (st[rkvs][rk]) = st[rk]])]]