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
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