Used simplifier rules: sub-trans: ⊦ s ⊆ s0 ∧ s0 ⊆ s1 → s ⊆ s1;%sub-ntrans-01: ⊦ s0 ⊆ s1 ∧ ¬ s ⊆ s1 → ¬ s ⊆ s0;