Nuprl Lemma : finite_functionality_wrt_equipollent
∀[A,B:Type]. (A ~ B ⇒ (finite(A) ⇐⇒ finite(B)))
Proof
Definitions occuring in Statement :
finite: finite(T),
equipollent: A ~ B,
uall: ∀[x:A]. B[x],
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
iff: P ⇐⇒ Q,
and: P ∧ Q,
finite: finite(T),
exists: ∃x:A. B[x],
member: t ∈ T,
guard: {T},
nat: ℕ,
prop: ℙ,
rev_implies: P ⇐ Q
Lemmas referenced :
equipollent_inversion,
equipollent_transitivity,
int_seg_wf,
equipollent_wf,
finite_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
independent_pairFormation,
sqequalHypSubstitution,
productElimination,
thin,
dependent_pairFormation,
hypothesisEquality,
cut,
introduction,
extract_by_obid,
isectElimination,
independent_functionElimination,
hypothesis,
natural_numberEquality,
setElimination,
rename,
cumulativity,
universeEquality
Latex:
\mforall{}[A,B:Type]. (A \msim{} B {}\mRightarrow{} (finite(A) \mLeftarrow{}{}\mRightarrow{} finite(B)))
Date html generated:
2016_10_21-AM-11_00_21
Last ObjectModification:
2016_08_06-PM-02_35_38
Theory : equipollence!!cardinality!
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