Nuprl Lemma : fun-connected_wf
∀[T:Type]. ∀[f:T ⟶ T]. ∀[x,y:T].  (y is f*(x) ∈ ℙ)
Proof
Definitions occuring in Statement : 
fun-connected: y is f*(x)
, 
uall: ∀[x:A]. B[x]
, 
prop: ℙ
, 
member: t ∈ T
, 
function: x:A ⟶ B[x]
, 
universe: Type
Definitions unfolded in proof : 
fun-connected: y is f*(x)
, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s]
Lemmas referenced : 
exists_wf, 
list_wf, 
fun-path_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalRule, 
sqequalReflexivity, 
sqequalTransitivity, 
computationStep, 
isect_memberFormation, 
introduction, 
cut, 
lemma_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
hypothesisEquality, 
hypothesis, 
lambdaEquality, 
axiomEquality, 
equalityTransitivity, 
equalitySymmetry, 
isect_memberEquality, 
because_Cache, 
functionEquality, 
universeEquality
Latex:
\mforall{}[T:Type].  \mforall{}[f:T  {}\mrightarrow{}  T].  \mforall{}[x,y:T].    (y  is  f*(x)  \mmember{}  \mBbbP{})
Date html generated:
2016_05_15-PM-04_58_01
Last ObjectModification:
2015_12_27-PM-02_30_08
Theory : general
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