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Proof step 9 from proof ADD-lemma (previous step)

s0 ≠ ∅, s0 ⊆ S, S3 = V0 ∪ (S \ s0), S2 = N0 ∪ (S \ (s0 ∪ V0)), s0 = s, ∀ w. ¬ w ∈ s0 ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
s0 ⊆ S, ∀ w. ¬ w ∈ s0 ⊦ # s0 = 0, s0 = ∅

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ # s ≠ 0 → s ≠ ∅], [CSIMPFORWARD : ⊦ s ≠ ∅ → # s ≠ 0])]]