Nuprl Lemma : equipollent_functionality_wrt_equipollent
∀[A1,A2,B1,B2:Type]. (A1 ~ A2 ⇒ B1 ~ B2 ⇒ (A1 ~ B1 ⇐⇒ A2 ~ B2))
Proof
Definitions occuring in Statement :
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,
member: t ∈ T,
guard: {T},
rev_implies: P ⇐ Q
Lemmas referenced :
equipollent_inversion,
equipollent_transitivity,
equipollent_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
independent_pairFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
independent_functionElimination,
hypothesis,
universeEquality
Latex:
\mforall{}[A1,A2,B1,B2:Type]. (A1 \msim{} A2 {}\mRightarrow{} B1 \msim{} B2 {}\mRightarrow{} (A1 \msim{} B1 \mLeftarrow{}{}\mRightarrow{} A2 \msim{} B2))
Date html generated:
2016_05_14-PM-04_00_13
Last ObjectModification:
2015_12_26-PM-07_44_30
Theory : equipollence!!cardinality!
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