Nuprl Lemma : equipollent-type-unit-pair
∀[T:Type]. T ~ T × Unit
Proof
Definitions occuring in Statement :
equipollent: A ~ B,
uall: ∀[x:A]. B[x],
unit: Unit,
product: x:A × B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
equipollent: A ~ B,
exists: ∃x:A. B[x],
biject: Bij(A;B;f),
surject: Surj(A;B;f),
inject: Inj(A;B;f),
and: P ∧ Q,
all: ∀x:A. B[x],
implies: P ⇒ Q,
pi1: fst(t),
prop: ℙ,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
top: Top
Lemmas referenced :
it_wf,
and_wf,
equal_wf,
unit_wf2,
pi1_wf_top,
subtype_rel_product,
top_wf,
biject_wf,
equal-unit
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
universeEquality,
dependent_pairFormation,
lambdaEquality,
independent_pairEquality,
hypothesisEquality,
cut,
lemma_by_obid,
hypothesis,
sqequalRule,
independent_pairFormation,
lambdaFormation,
equalitySymmetry,
dependent_set_memberEquality,
equalityTransitivity,
sqequalHypSubstitution,
isectElimination,
thin,
productEquality,
applyEquality,
setElimination,
rename,
productElimination,
because_Cache,
independent_isectElimination,
isect_memberEquality,
voidElimination,
voidEquality,
setEquality
Latex:
\mforall{}[T:Type]. T \msim{} T \mtimes{} Unit
Date html generated:
2016_05_15-PM-06_06_44
Last ObjectModification:
2015_12_27-PM-00_16_03
Theory : general
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