Nuprl Lemma : product-subtype-co-list
∀[T:Type]. ((T × colist(T)) ⊆r colist(T))
Proof
Definitions occuring in Statement :
colist: colist(T),
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
product: 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,
ext-eq: A ≡ B,
and: P ∧ Q
Lemmas referenced :
subtype_rel_transitivity,
colist_wf,
b-union_wf,
unit_wf2,
subtype_rel_b-union-right,
istype-universe,
colist-ext
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
productEquality,
hypothesisEquality,
hypothesis,
independent_isectElimination,
because_Cache,
sqequalRule,
axiomEquality,
instantiate,
universeEquality,
productElimination
Latex:
\mforall{}[T:Type]. ((T \mtimes{} colist(T)) \msubseteq{}r colist(T))
Date html generated:
2019_10_16-AM-11_38_09
Last ObjectModification:
2019_06_26-PM-04_07_05
Theory : eval!all
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