Predicate Calculus for Boolean Valued Functions. Part IX
نویسنده
چکیده
The terminology and notation used in this paper are introduced in the following papers: [1], [2], [3], [4], and [5]. In this paper Y is a non empty set. The following propositions are true: (1) Let a be an element of BVF(Y ), G be a subset of PARTITIONS(Y ), and A, B, C be partitions of Y . Suppose G is a coordinate and G = {A, B,C} and A 6= B and B 6= C and C 6= A. Then ¬∃∃a,AG,BG ⋐ ¬∃∃a,BG,AG. (2) Let a be an element of BVF(Y ), G be a subset of PARTITIONS(Y ), and A, B, C be partitions of Y . Suppose G is a coordinate and G = {A, B,C} and A 6= B and B 6= C and C 6= A. Then ¬∀∀a,AG,BG ⋐ ¬∀∀a,BG,AG. (3) Let a be an element of BVF(Y ), G be a subset of PARTITIONS(Y ), and A, B, C be partitions of Y . Suppose G is a coordinate and G = {A, B,C} and A 6= B and B 6= C and C 6= A. Then ¬∃∀a,AG,BG ⋐ ¬∀∀a,BG,AG. (4) Let a be an element of BVF(Y ), G be a subset of PARTITIONS(Y ), and A, B, C be partitions of Y . Suppose G is a coordinate and G = {A, B,C} and A 6= B and B 6= C and C 6= A. Then ¬∀∃a,AG,BG ⋐ ¬∀∀a,BG,AG. (5) Let a be an element of BVF(Y ), G be a subset of PARTITIONS(Y ), and A, B, C be partitions of Y . Suppose G is a coordinate and G = {A, B,C} and A 6= B and B 6= C and C 6= A. Then ¬∃∃a,AG,BG ⋐ ¬∀∀a,BG,AG.
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