Nuprl Lemma : product_functionality_wrt_equipollent
∀[A,B,C,D:Type]. (A ~ B ⇒ C ~ D ⇒ A × C ~ B × D)
Proof
Definitions occuring in Statement :
equipollent: A ~ B,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
product: x:A × B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
member: t ∈ T,
uimplies: b supposing a,
guard: {T}
Lemmas referenced :
product_functionality_wrt_equipollent_right,
equipollent_wf,
product_functionality_wrt_equipollent_left,
equipollent_transitivity
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
because_Cache,
hypothesisEquality,
independent_functionElimination,
hypothesis,
universeEquality,
independent_isectElimination,
productEquality
Latex:
\mforall{}[A,B,C,D:Type]. (A \msim{} B {}\mRightarrow{} C \msim{} D {}\mRightarrow{} A \mtimes{} C \msim{} B \mtimes{} D)
Date html generated:
2016_05_14-PM-04_00_00
Last ObjectModification:
2015_12_26-PM-07_44_31
Theory : equipollence!!cardinality!
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