Nuprl Lemma : finite-indep-fun
∀S,T:Type.  (finite(S) 
⇒ finite(T) 
⇒ finite(S ⟶ T))
Proof
Definitions occuring in Statement : 
finite: finite(T)
, 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
, 
function: x:A ⟶ B[x]
, 
universe: Type
Definitions unfolded in proof : 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
, 
member: t ∈ T
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s]
, 
prop: ℙ
, 
uall: ∀[x:A]. B[x]
Lemmas referenced : 
finite-function, 
finite_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
lambdaFormation, 
cut, 
introduction, 
extract_by_obid, 
sqequalHypSubstitution, 
dependent_functionElimination, 
thin, 
hypothesisEquality, 
sqequalRule, 
lambdaEquality, 
cumulativity, 
independent_functionElimination, 
hypothesis, 
because_Cache, 
isectElimination, 
universeEquality
Latex:
\mforall{}S,T:Type.    (finite(S)  {}\mRightarrow{}  finite(T)  {}\mRightarrow{}  finite(S  {}\mrightarrow{}  T))
Date html generated:
2016_10_21-AM-11_00_36
Last ObjectModification:
2016_08_06-PM-04_53_58
Theory : equipollence!!cardinality!
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