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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