Nuprl Lemma : equipollent-identity-right
∀[A:Type]. A × Top ~ A
Proof
Definitions occuring in Statement :
equipollent: A ~ B,
uall: ∀[x:A]. B[x],
top: Top,
product: x:A × B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
implies: P ⇒ Q,
uimplies: b supposing a,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
top_wf,
equipollent-identity-left,
equipollent_functionality_wrt_equipollent,
equipollent-product-com,
equipollent_weakening_ext-eq,
ext-eq_weakening
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
universeEquality,
productEquality,
hypothesisEquality,
thin,
cut,
lemma_by_obid,
hypothesis,
because_Cache,
sqequalHypSubstitution,
isectElimination,
independent_functionElimination,
independent_isectElimination,
productElimination
Latex:
\mforall{}[A:Type]. A \mtimes{} Top \msim{} A
Date html generated:
2016_05_14-PM-04_01_01
Last ObjectModification:
2015_12_26-PM-07_43_45
Theory : equipollence!!cardinality!
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