Nuprl Lemma : colist-value-type
∀[T:Type]. value-type(colist(T))
Proof
Definitions occuring in Statement :
colist: colist(T),
value-type: value-type(T),
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
unit: Unit,
so_lambda: λ2x.t[x],
so_apply: x[s],
value-type: value-type(T),
has-value: (a)↓,
prop: ℙ
Lemmas referenced :
value-type_functionality,
colist_wf,
b-union_wf,
unit_wf2,
colist-ext,
bunion-value-type,
equal-value-type,
product-value-type,
equal-wf-base,
base_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
productEquality,
independent_isectElimination,
productElimination,
independent_functionElimination,
sqequalRule,
intEquality,
natural_numberEquality,
because_Cache,
lambdaEquality,
isect_memberEquality,
axiomSqleEquality,
equalityTransitivity,
equalitySymmetry,
universeEquality
Latex:
\mforall{}[T:Type]. value-type(colist(T))
Date html generated:
2016_05_14-AM-06_25_23
Last ObjectModification:
2015_12_26-PM-00_42_31
Theory : list_0
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