Nuprl Lemma : equipollent-product-assoc
∀[A,B,C:Type]. A × B × C ~ A × B × C
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,
spreadn: spread3,
prop: ℙ,
biject: Bij(A;B;f),
and: P ∧ Q,
inject: Inj(A;B;f),
all: ∀x:A. B[x],
implies: P ⇒ Q,
pi1: fst(t),
so_lambda: λ2x.t[x],
so_apply: x[s],
pi2: snd(t),
surject: Surj(A;B;f)
Lemmas referenced :
biject_wf,
and_wf,
equal_wf,
pi1_wf,
pi2_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
dependent_pairFormation,
lambdaEquality,
productElimination,
thin,
sqequalRule,
independent_pairEquality,
hypothesisEquality,
productEquality,
cumulativity,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesis,
universeEquality,
independent_pairFormation,
lambdaFormation,
equalitySymmetry,
dependent_set_memberEquality,
equalityTransitivity,
applyEquality,
setElimination,
rename,
setEquality
Latex:
\mforall{}[A,B,C:Type]. A \mtimes{} B \mtimes{} C \msim{} A \mtimes{} B \mtimes{} C
Date html generated:
2016_05_14-PM-04_00_37
Last ObjectModification:
2015_12_26-PM-07_44_15
Theory : equipollence!!cardinality!
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