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Proof step 4 from proof validmode-put-nonnull (previous step)

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

Heuristic simplifier applied rule simplifier

And closed the goal!

Rule argument

[emptyarg]

Additional information

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