Nuprl Lemma : per-class-subtype-singleton
∀[T:Type]. ∀[a:T]. (per-class(T;a) ⊆r {x:T| x = a ∈ T} )
Proof
Definitions occuring in Statement :
per-class: per-class(T;a),
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
set: {x:A| B[x]} ,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
per-class: per-class(T;a),
prop: ℙ
Lemmas referenced :
equal_wf,
per-class_wf,
subtype_rel_b-union-right,
base_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaEquality,
sqequalHypSubstitution,
setElimination,
thin,
rename,
dependent_set_memberEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
extract_by_obid,
isectElimination,
cumulativity,
hypothesisEquality,
applyEquality,
because_Cache,
sqequalRule,
axiomEquality,
isect_memberEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[a:T]. (per-class(T;a) \msubseteq{}r \{x:T| x = a\} )
Date html generated:
2017_04_14-AM-07_37_02
Last ObjectModification:
2017_02_27-PM-03_09_11
Theory : subtype_1
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