Nuprl Lemma : subtype_rel-equal
∀[A,B:Type]. A ⊆r B supposing A = B ∈ Type
Proof
Definitions occuring in Statement :
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
member: t ∈ T,
subtype_rel: A ⊆r B,
prop: ℙ
Lemmas referenced :
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
cut,
equalityTransitivity,
hypothesis,
equalitySymmetry,
lambdaEquality,
hyp_replacement,
hypothesisEquality,
thin,
instantiate,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
universeEquality
Latex:
\mforall{}[A,B:Type]. A \msubseteq{}r B supposing A = B
Date html generated:
2017_04_14-AM-07_14_05
Last ObjectModification:
2017_02_27-PM-02_49_58
Theory : subtype_0
Home
Index