Nuprl Lemma : corec-family_wf
∀[P:Type]. ∀[H:(P ⟶ Type) ⟶ P ⟶ Type].  (corec-family(H) ∈ P ⟶ Type)
Proof
Definitions occuring in Statement : 
corec-family: corec-family(H)
, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
function: x:A ⟶ B[x]
, 
universe: Type
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
corec-family: corec-family(H)
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s]
Lemmas referenced : 
isect-family_wf, 
nat_wf, 
fun_exp_wf, 
top_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
sqequalRule, 
lemma_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
hypothesisEquality, 
hypothesis, 
lambdaEquality, 
applyEquality, 
instantiate, 
functionEquality, 
cumulativity, 
universeEquality, 
axiomEquality, 
equalityTransitivity, 
equalitySymmetry, 
isect_memberEquality, 
because_Cache
Latex:
\mforall{}[P:Type].  \mforall{}[H:(P  {}\mrightarrow{}  Type)  {}\mrightarrow{}  P  {}\mrightarrow{}  Type].    (corec-family(H)  \mmember{}  P  {}\mrightarrow{}  Type)
Date html generated:
2016_05_14-AM-06_12_18
Last ObjectModification:
2015_12_26-PM-00_06_09
Theory : co-recursion
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