Nuprl Lemma : corec-family-ext
∀[P:Type]. ∀[H:(P ⟶ Type) ⟶ P ⟶ Type].
corec-family(H) ≡ H corec-family(H) supposing type-family-continuous{i:l}(P;H) ∧ family-monotone{i:l}(P;H)
Proof
Definitions occuring in Statement :
corec-family: corec-family(H),
type-family-continuous: type-family-continuous{i:l}(P;H),
family-monotone: family-monotone{i:l}(P;H),
ext-family: F ≡ G,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
and: P ∧ Q,
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,
and: P ∧ Q,
uiff: uiff(P;Q),
cand: A c∧ B,
ext-family: F ≡ G,
all: ∀x:A. B[x],
ext-eq: A ≡ B,
subtype_rel: A ⊆r B,
prop: ℙ
Lemmas referenced :
ext-family-iff,
corec-family_wf,
sub-corec-family,
corec-sub-family,
and_wf,
type-family-continuous_wf,
family-monotone_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
productElimination,
thin,
lemma_by_obid,
isectElimination,
hypothesisEquality,
hypothesis,
applyEquality,
independent_isectElimination,
because_Cache,
independent_pairFormation,
sqequalRule,
lambdaEquality,
dependent_functionElimination,
independent_pairEquality,
axiomEquality,
instantiate,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
cumulativity,
universeEquality
Latex:
\mforall{}[P:Type]. \mforall{}[H:(P {}\mrightarrow{} Type) {}\mrightarrow{} P {}\mrightarrow{} Type].
corec-family(H) \mequiv{} H corec-family(H)
supposing type-family-continuous\{i:l\}(P;H) \mwedge{} family-monotone\{i:l\}(P;H)
Date html generated:
2016_05_14-AM-06_12_25
Last ObjectModification:
2015_12_26-PM-00_06_07
Theory : co-recursion
Home
Index