Nuprl Lemma : urec-is-fixedpoint
∀[F:Type ⟶ Type]. F urec(F) ≡ urec(F) supposing continuous'-monotone{i:l}(T.F T)
Proof
Definitions occuring in Statement :
continuous'-monotone: continuous'-monotone{i:l}(T.F[T]),
urec: urec(F),
ext-eq: A ≡ B,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
apply: f a,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
ext-eq: A ≡ B,
and: P ∧ Q,
continuous'-monotone: continuous'-monotone{i:l}(T.F[T]),
so_apply: x[s],
subtype_rel: A ⊆r B,
prop: ℙ,
so_lambda: λ2x.t[x]
Lemmas referenced :
subtype_urec,
urec_subtype,
continuous'-monotone_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
independent_pairFormation,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
independent_isectElimination,
hypothesis,
productElimination,
sqequalRule,
independent_pairEquality,
axiomEquality,
lambdaEquality,
applyEquality,
universeEquality,
isect_memberEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
functionEquality
Latex:
\mforall{}[F:Type {}\mrightarrow{} Type]. F urec(F) \mequiv{} urec(F) supposing continuous'-monotone\{i:l\}(T.F T)
Date html generated:
2016_05_15-PM-06_54_38
Last ObjectModification:
2015_12_27-AM-11_41_23
Theory : general
Home
Index