Nuprl Lemma : equipollent_weakening
∀[A,B:Type]. A ~ B supposing A = B ∈ Type
Proof
Definitions occuring in Statement :
equipollent: A ~ B,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
equipollent: A ~ B,
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
member: t ∈ T,
exists: ∃x:A. B[x],
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
id-biject,
biject_wf,
exists_wf,
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
cut,
introduction,
axiomEquality,
hypothesis,
thin,
rename,
dependent_pairFormation,
lambdaEquality,
hypothesisEquality,
cumulativity,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
functionExtensionality,
applyEquality,
hyp_replacement,
equalitySymmetry,
Error :applyLambdaEquality,
functionEquality,
instantiate,
universeEquality
Latex:
\mforall{}[A,B:Type]. A \msim{} B supposing A = B
Date html generated:
2016_10_21-AM-10_51_53
Last ObjectModification:
2016_07_12-AM-05_55_49
Theory : equipollence!!cardinality!
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