Nuprl Lemma : subtype_rel_wf
∀[A,B:Type]. (A ⊆r B ∈ Type)
Proof
Definitions occuring in Statement :
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
prop: ℙ
Lemmas referenced :
equal-wf-base
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
hypothesis,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeEquality,
isect_memberEquality,
isectElimination,
thin,
hypothesisEquality,
because_Cache,
functionEquality,
baseClosed,
lemma_by_obid
Latex:
\mforall{}[A,B:Type]. (A \msubseteq{}r B \mmember{} Type)
Date html generated:
2016_05_13-PM-03_06_47
Last ObjectModification:
2016_01_06-PM-05_28_54
Theory : core_2
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