Nuprl Lemma : finite_functionality_wrt_ext-eq
∀[A,B:Type]. (A ≡ B ⇒ (finite(A) ⇐⇒ finite(B)))
Proof
Definitions occuring in Statement :
finite: finite(T),
ext-eq: 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,
nat: ℕ,
prop: ℙ,
rev_implies: P ⇐ Q,
guard: {T},
uimplies: b supposing a
Lemmas referenced :
equipollent_wf,
int_seg_wf,
finite_wf,
ext-eq_wf,
ext-eq_inversion,
equipollent_transitivity,
equipollent_weakening_ext-eq
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,
natural_numberEquality,
setElimination,
rename,
hypothesis,
universeEquality,
independent_isectElimination,
independent_functionElimination
Latex:
\mforall{}[A,B:Type]. (A \mequiv{} B {}\mRightarrow{} (finite(A) \mLeftarrow{}{}\mRightarrow{} finite(B)))
Date html generated:
2019_06_20-PM-02_18_56
Last ObjectModification:
2018_09_24-PM-01_01_08
Theory : equipollence!!cardinality!
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