Nuprl Lemma : squash-per-class
∀[T:Type]. ∀[a:T]. (↓per-class(T;a))
Proof
Definitions occuring in Statement :
per-class: per-class(T;a),
uall: ∀[x:A]. B[x],
squash: ↓T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
squash: ↓T,
per-class: per-class(T;a),
prop: ℙ,
uimplies: b supposing a,
guard: {T},
implies: P ⇒ Q,
subtype_rel: A ⊆r B,
true: True
Lemmas referenced :
b-union_wf,
equal_functionality_wrt_subtype_rel2,
base_wf,
subtype_rel_b-union-right,
per-class_wf,
true_wf,
squash_wf,
equal-wf-base-T
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
hypothesis,
sqequalHypSubstitution,
imageElimination,
sqequalRule,
imageMemberEquality,
hypothesisEquality,
thin,
baseClosed,
isect_memberEquality,
isectElimination,
because_Cache,
universeEquality,
pointwiseFunctionality,
dependent_set_memberEquality,
equalityTransitivity,
equalitySymmetry,
lemma_by_obid,
applyEquality,
lambdaEquality,
independent_isectElimination,
independent_functionElimination,
natural_numberEquality
Latex:
\mforall{}[T:Type]. \mforall{}[a:T]. (\mdownarrow{}per-class(T;a))
Date html generated:
2016_05_13-PM-04_12_34
Last ObjectModification:
2016_01_14-PM-07_29_30
Theory : subtype_1
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