Nuprl Lemma : subtype_rel_functionality_wrt_iff

[A,B,C,D:Type].  ({uiff(A ⊆B;C ⊆D)}) supposing (B ≡ and A ≡ C)


Definitions occuring in Statement :  ext-eq: A ≡ B uiff: uiff(P;Q) uimplies: supposing a subtype_rel: A ⊆B uall: [x:A]. B[x] guard: {T} universe: Type
Definitions unfolded in proof :  guard: {T} ext-eq: A ≡ B uall: [x:A]. B[x] member: t ∈ T uimplies: supposing a and: P ∧ Q uiff: uiff(P;Q) subtype_rel: A ⊆B prop:
Lemmas referenced :  subtype_rel_transitivity subtype_rel_wf and_wf
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep isect_memberFormation introduction cut sqequalHypSubstitution productElimination thin independent_pairFormation hypothesis lemma_by_obid isectElimination hypothesisEquality independent_isectElimination axiomEquality independent_pairEquality isect_memberEquality equalityTransitivity equalitySymmetry because_Cache universeEquality

\mforall{}[A,B,C,D:Type].    (\{uiff(A  \msubseteq{}r  B;C  \msubseteq{}r  D)\})  supposing  (B  \mequiv{}  D  and  A  \mequiv{}  C)

Date html generated: 2016_05_13-PM-03_19_08
Last ObjectModification: 2015_12_26-AM-09_07_52

Theory : subtype_0

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