Nuprl Lemma : equipollent-product-com
∀[A,B:Type]. A × B ~ B × A
Proof
Definitions occuring in Statement :
equipollent: A ~ B,
uall: ∀[x:A]. B[x],
product: x:A × B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
equipollent: A ~ B,
exists: ∃x:A. B[x],
member: t ∈ T,
biject: Bij(A;B;f),
and: P ∧ Q,
inject: Inj(A;B;f),
all: ∀x:A. B[x],
implies: P ⇒ Q,
prop: ℙ,
surject: Surj(A;B;f),
so_lambda: λ2x.t[x],
so_apply: x[s],
pi2: snd(t),
pi1: fst(t)
Lemmas referenced :
equal_wf,
biject_wf,
pi2_wf,
pi1_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
dependent_pairFormation,
lambdaEquality,
spreadEquality,
hypothesisEquality,
independent_pairEquality,
productEquality,
thin,
independent_pairFormation,
lambdaFormation,
sqequalRule,
cut,
hypothesis,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
universeEquality,
productElimination,
applyEquality,
equalityUniverse,
levelHypothesis,
because_Cache,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[A,B:Type]. A \mtimes{} B \msim{} B \mtimes{} A
Date html generated:
2016_05_14-PM-04_00_39
Last ObjectModification:
2015_12_26-PM-07_44_00
Theory : equipollence!!cardinality!
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