Nuprl Lemma : product-equipollent-tuple
∀[A,B:Type]. A × B ~ tuple-type([A; B])
Proof
Definitions occuring in Statement :
equipollent: A ~ B,
tuple-type: tuple-type(L),
cons: [a / b],
nil: [],
uall: ∀[x:A]. B[x],
product: x:A × B[x],
universe: Type
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
top: Top,
ifthenelse: if b then t else f fi ,
bfalse: ff,
btrue: tt,
uall: ∀[x:A]. B[x],
uimplies: b supposing a
Lemmas referenced :
tupletype_cons_lemma,
null_cons_lemma,
null_nil_lemma,
tupletype_nil_lemma,
equipollent_weakening_ext-eq,
ext-eq_weakening
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
cut,
lemma_by_obid,
sqequalHypSubstitution,
sqequalTransitivity,
computationStep,
dependent_functionElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
isect_memberFormation,
universeEquality,
productEquality,
hypothesisEquality,
isectElimination,
independent_isectElimination
Latex:
\mforall{}[A,B:Type]. A \mtimes{} B \msim{} tuple-type([A; B])
Date html generated:
2016_05_15-PM-05_50_28
Last ObjectModification:
2015_12_27-PM-00_27_29
Theory : general
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