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. Eq, =? (c 1 ? ?(n) ? c 2 ? ?(n)) =? u ? ?(n)) =? ? |= ccsl c 1 ? un)) =? ? |= ccsl c 2 ? u. Proof of Proposition 24: Let us assume ? |= ccsl i c 1 * c 2 . (i ? ?(n) =? (c 1 ? ?(n) ? c 2 ? ?(n)) =? c 1 ? ?(n)) =? ? |= ccsl i ? c 1 . (i ? ?(n) =? (c 1 ? ?(n) ? c 2 ? ?(n)) =? c 2 ? ?(n)) =? ? |= ccsl i ? c 2 . Proof of Proposition 26: Let us assume ? |= ccsl inf c 1 ? c 2 . (? ? (inf, n) = max(? ? (c 1 , n), ? ? (c2 , n)) =? ? ? (inf, n) ? ? ? (c 1 , n)) =? ? |= ccsl inf c 1 . Similarly, ? ? (inf, n) ? ? ?, Proof of Proposition =? ? |= ccsl inf c 2 . Proof of Proposition 27: Let us assume ? |= ccsl sup c 1 ? c 2 . (? ? (sup, n) = min(? ? (c 1 , n), ? ? (c2 , n)) =? ? ? (c 1 , n) ? ? ? (sup, n)) =? ? |= ccsl c 1 sup. Similarly, ? ? (c 2 , n) ? ? ? (sup, n)) =? ? |= ccsl c 2 sup