Nuprl Lemma : fun_exp_wf
∀[T:Type]. ∀[n:ℕ]. ∀[f:T ⟶ T].  (f^n ∈ T ⟶ T)
Proof
Definitions occuring in Statement : 
fun_exp: f^n
, 
nat: ℕ
, 
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
, 
fun_exp: f^n
, 
nat: ℕ
Lemmas referenced : 
primrec_wf, 
compose_wf, 
int_seg_wf, 
nat_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
Error :isect_memberFormation_alt, 
introduction, 
cut, 
sqequalRule, 
extract_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
functionEquality, 
hypothesisEquality, 
lambdaEquality, 
hypothesis, 
natural_numberEquality, 
setElimination, 
rename, 
axiomEquality, 
equalityTransitivity, 
equalitySymmetry, 
Error :functionIsType, 
Error :universeIsType, 
Error :inhabitedIsType, 
isect_memberEquality, 
because_Cache, 
universeEquality
Latex:
\mforall{}[T:Type].  \mforall{}[n:\mBbbN{}].  \mforall{}[f:T  {}\mrightarrow{}  T].    (f\^{}n  \mmember{}  T  {}\mrightarrow{}  T)
Date html generated:
2019_06_20-PM-00_26_38
Last ObjectModification:
2018_09_26-AM-11_48_50
Theory : fun_1
Home
Index