Nuprl Lemma : param-co-W_wf
∀[P:Type]. ∀[A:P ⟶ Type]. ∀[B:p:P ⟶ A[p] ⟶ Type]. ∀[C:p:P ⟶ a:A[p] ⟶ B[p;a] ⟶ P]. (pco-W ∈ P ⟶ Type)
Proof
Definitions occuring in Statement :
param-co-W: pco-W,
uall: ∀[x:A]. B[x],
so_apply: x[s1;s2;s3],
so_apply: x[s1;s2],
so_apply: x[s],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
param-co-W: pco-W,
so_apply: x[s],
so_apply: x[s1;s2],
so_apply: x[s1;s2;s3]
Lemmas referenced :
corec-family_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
lambdaEquality,
productEquality,
applyEquality,
functionEquality,
cumulativity,
universeEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[P:Type]. \mforall{}[A:P {}\mrightarrow{} Type]. \mforall{}[B:p:P {}\mrightarrow{} A[p] {}\mrightarrow{} Type]. \mforall{}[C:p:P {}\mrightarrow{} a:A[p] {}\mrightarrow{} B[p;a] {}\mrightarrow{} P].
(pco-W \mmember{} P {}\mrightarrow{} Type)
Date html generated:
2016_05_14-AM-06_12_27
Last ObjectModification:
2015_12_26-PM-00_06_05
Theory : co-recursion
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