Nuprl Lemma : trivial-per-class
∀[T:Type]. ∀[a:T ⋂ Base]. (a ∈ per-class(T;a))
Proof
Definitions occuring in Statement :
per-class: per-class(T;a),
isect2: T1 ⋂ T2,
uall: ∀[x:A]. B[x],
member: t ∈ T,
base: Base,
universe: Type
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 :
isect2_subtype_rel,
base_wf,
isect2_subtype_rel2,
equal-wf-base-T,
isect2_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
hypothesisEquality,
applyEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
sqequalRule,
dependent_set_memberEquality,
equalityTransitivity,
equalitySymmetry,
axiomEquality,
isect_memberEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[a:T \mcap{} Base]. (a \mmember{} per-class(T;a))
Date html generated:
2016_05_13-PM-04_12_32
Last ObjectModification:
2015_12_26-AM-11_12_16
Theory : subtype_1
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