Nuprl Lemma : subtype_rel_transitivity
∀[A,B,C:Type]. (A ⊆r C) supposing ((B ⊆r C) and (A ⊆r B))
Proof
Definitions occuring in Statement :
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
subtype_rel: A ⊆r B
Lemmas referenced :
subtype_rel_wf,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
axiomEquality,
hypothesis,
universeIsType,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
isect_memberEquality_alt,
isectIsTypeImplies,
inhabitedIsType,
instantiate,
universeEquality,
lambdaEquality_alt,
applyEquality
Latex:
\mforall{}[A,B,C:Type]. (A \msubseteq{}r C) supposing ((B \msubseteq{}r C) and (A \msubseteq{}r B))
Date html generated:
2020_05_19-PM-09_35_10
Last ObjectModification:
2019_12_05-PM-00_02_01
Theory : subtype_0
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