Nuprl Lemma : colist-ext
∀[T:Type]. colist(T) ≡ Unit ⋃ (T × colist(T))
Proof
Definitions occuring in Statement :
colist: colist(T),
b-union: A ⋃ B,
ext-eq: A ≡ B,
uall: ∀[x:A]. B[x],
unit: Unit,
product: x:A × B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
colist: colist(T),
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
ext-eq: A ≡ B,
and: P ∧ Q,
subtype_rel: A ⊆r B
Lemmas referenced :
corec-ext,
b-union_wf,
unit_wf2,
list-functor
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
sqequalRule,
lambdaEquality,
hypothesis,
productEquality,
hypothesisEquality,
universeEquality,
independent_isectElimination,
productElimination,
independent_pairEquality,
axiomEquality
Latex:
\mforall{}[T:Type]. colist(T) \mequiv{} Unit \mcup{} (T \mtimes{} colist(T))
Date html generated:
2016_05_14-AM-06_25_22
Last ObjectModification:
2015_12_26-PM-00_42_32
Theory : list_0
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