Nuprl Lemma : copath_wf
∀[A:𝕌']. ∀[B:A ⟶ Type]. ∀[w:coW(A;a.B[a])].  (copath(a.B[a];w) ∈ Type)
Proof
Definitions occuring in Statement : 
copath: copath(a.B[a];w)
, 
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
, 
copath: copath(a.B[a];w)
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s]
Lemmas referenced : 
nat_wf, 
coPath_wf, 
coW_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
sqequalRule, 
productEquality, 
extract_by_obid, 
hypothesis, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
hypothesisEquality, 
lambdaEquality, 
applyEquality, 
axiomEquality, 
equalityTransitivity, 
equalitySymmetry, 
instantiate, 
cumulativity, 
isect_memberEquality, 
because_Cache, 
functionEquality, 
universeEquality
Latex:
\mforall{}[A:\mBbbU{}'].  \mforall{}[B:A  {}\mrightarrow{}  Type].  \mforall{}[w:coW(A;a.B[a])].    (copath(a.B[a];w)  \mmember{}  Type)
Date html generated:
2018_07_25-PM-01_38_49
Last ObjectModification:
2018_06_01-AM-08_39_19
Theory : co-recursion
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