Nuprl Lemma : isect2_subtype_rel
∀[A,B:Type]. (A ⋂ B ⊆r A)
Proof
Definitions occuring in Statement :
isect2: T1 ⋂ T2,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
and: P ∧ Q,
cand: A c∧ B
Lemmas referenced :
isect2_decomp,
isect2_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
productElimination,
equalityTransitivity,
hypothesis,
equalitySymmetry,
independent_pairFormation,
sqequalRule,
axiomEquality,
universeEquality,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[A,B:Type]. (A \mcap{} B \msubseteq{}r A)
Date html generated:
2016_05_13-PM-03_58_06
Last ObjectModification:
2015_12_26-AM-10_51_31
Theory : bool_1
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