Nuprl Lemma : equipollent-identity
∀[A,B:Type]. (B ~ Unit ⇒ B × A ~ A)
Proof
Definitions occuring in Statement :
equipollent: A ~ B,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
unit: Unit,
product: x:A × B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
equipollent: A ~ B,
exists: ∃x:A. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
so_apply: x[s],
biject: Bij(A;B;f),
and: P ∧ Q,
inject: Inj(A;B;f),
all: ∀x:A. B[x],
prop: ℙ,
surject: Surj(A;B;f),
pi2: snd(t)
Lemmas referenced :
pi2_wf,
equal_wf,
biject_wf,
equipollent_wf,
unit_wf2,
equal-unit,
it_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
dependent_pairFormation,
lambdaEquality,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
sqequalRule,
hypothesis,
productEquality,
independent_pairFormation,
universeEquality,
productElimination,
independent_pairEquality,
dependent_functionElimination,
independent_functionElimination,
applyEquality
Latex:
\mforall{}[A,B:Type]. (B \msim{} Unit {}\mRightarrow{} B \mtimes{} A \msim{} A)
Date html generated:
2016_05_14-PM-04_00_54
Last ObjectModification:
2015_12_26-PM-07_43_54
Theory : equipollence!!cardinality!
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