Nuprl Lemma : dep-isect-subtype

A:Type. ∀B:A ⟶ Type.  (x:A ⋂ B[x] ⊆A)


Proof




Definitions occuring in Statement :  dep-isect: x:A ⋂ B[x] subtype_rel: A ⊆B so_apply: x[s] all: x:A. B[x] function: x:A ⟶ B[x] universe: Type
Definitions unfolded in proof :  all: x:A. B[x] subtype_rel: A ⊆B member: t ∈ T so_lambda: λ2x.t[x] so_apply: x[s]
Lemmas referenced :  dep-isect_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity lambdaFormation lambdaEquality dependentIntersectionElimination sqequalHypSubstitution equalityTransitivity hypothesis equalitySymmetry cut lemma_by_obid dependent_functionElimination thin cumulativity hypothesisEquality sqequalRule applyEquality functionEquality universeEquality

Latex:
\mforall{}A:Type.  \mforall{}B:A  {}\mrightarrow{}  Type.    (x:A  \mcap{}  B[x]  \msubseteq{}r  A)



Date html generated: 2016_05_15-PM-02_07_04
Last ObjectModification: 2015_12_27-AM-00_28_08

Theory : dependent!intersection


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