Nuprl Lemma : coW_wf
∀[A:Type]. ∀[B:A ⟶ Type]. (coW(A;a.B[a]) ∈ Type)
Proof
Definitions occuring in Statement :
coW: coW(A;a.B[a]),
uall: ∀[x:A]. B[x],
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,
coW: coW(A;a.B[a]),
so_lambda: λ2x.t[x],
so_apply: x[s],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
so_lambda: so_lambda(x,y,z.t[x; y; z]),
top: Top,
so_apply: x[s1;s2;s3]
Lemmas referenced :
param-co-W_wf,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
applyEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
lambdaEquality,
hypothesisEquality,
isect_memberEquality,
voidElimination,
voidEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
cumulativity,
universeEquality,
because_Cache
Latex:
\mforall{}[A:Type]. \mforall{}[B:A {}\mrightarrow{} Type]. (coW(A;a.B[a]) \mmember{} Type)
Date html generated:
2018_07_25-PM-01_37_08
Last ObjectModification:
2018_05_31-PM-04_21_12
Theory : co-recursion
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