Nuprl Lemma : equipollent_weakening_ext-eq
∀[A,B:Type]. A ~ B supposing A ≡ B
Proof
Definitions occuring in Statement :
equipollent: A ~ B,
ext-eq: A ≡ B,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
member: t ∈ T,
ext-eq: A ≡ B,
and: P ∧ Q,
subtype_rel: A ⊆r B,
equipollent: A ~ B,
exists: ∃x:A. B[x],
biject: Bij(A;B;f),
inject: Inj(A;B;f),
all: ∀x:A. B[x],
implies: P ⇒ Q,
guard: {T},
prop: ℙ,
surject: Surj(A;B;f)
Lemmas referenced :
equal_functionality_wrt_subtype_rel2,
equal_wf,
biject_wf,
ext-eq_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
cut,
introduction,
sqequalRule,
sqequalHypSubstitution,
productElimination,
thin,
independent_pairEquality,
axiomEquality,
hypothesis,
rename,
dependent_pairFormation,
lambdaEquality,
hypothesisEquality,
applyEquality,
independent_pairFormation,
lambdaFormation,
lemma_by_obid,
isectElimination,
equalityTransitivity,
equalitySymmetry,
independent_isectElimination,
independent_functionElimination,
universeEquality
Latex:
\mforall{}[A,B:Type]. A \msim{} B supposing A \mequiv{} B
Date html generated:
2016_05_14-PM-04_00_11
Last ObjectModification:
2015_12_26-PM-07_44_32
Theory : equipollence!!cardinality!
Home
Index