Nuprl Lemma : co-w-ext
∀[A:Type]. co-w(A) ≡ Unit + (A ⟶ co-w(A))
Proof
Definitions occuring in Statement :
co-w: co-w(A),
ext-eq: A ≡ B,
uall: ∀[x:A]. B[x],
unit: Unit,
function: x:A ⟶ B[x],
union: left + right,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
co-w: co-w(A),
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
all: ∀x:A. B[x],
implies: P ⇒ Q,
ext-eq: A ≡ B,
and: P ∧ Q,
subtype_rel: A ⊆r B
Lemmas referenced :
corec-ext,
unit_wf2,
continuous-monotone-union,
continuous-monotone-constant,
continuous-monotone-function,
continuous-monotone-id
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
sqequalRule,
lambdaEquality,
unionEquality,
hypothesis,
functionEquality,
hypothesisEquality,
universeEquality,
independent_isectElimination,
dependent_functionElimination,
independent_functionElimination,
productElimination,
independent_pairEquality,
axiomEquality
Latex:
\mforall{}[A:Type]. co-w(A) \mequiv{} Unit + (A {}\mrightarrow{} co-w(A))
Date html generated:
2016_05_15-PM-10_05_35
Last ObjectModification:
2015_12_27-PM-05_50_42
Theory : bar!induction
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