Nuprl Lemma : equipollent_inversion
∀[A,B:Type]. (A ~ B ⇒ B ~ A)
Proof
Definitions occuring in Statement :
equipollent: A ~ B,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
universe: Type
Definitions unfolded in proof :
equipollent: A ~ B,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
exists: ∃x:A. B[x],
biject: Bij(A;B;f),
and: P ∧ Q,
member: t ∈ T,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
surject: Surj(A;B;f),
all: ∀x:A. B[x],
pi1: fst(t),
inject: Inj(A;B;f),
guard: {T}
Lemmas referenced :
exists_wf,
biject_wf,
equal_wf,
all_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
lambdaFormation,
sqequalHypSubstitution,
productElimination,
thin,
cut,
introduction,
extract_by_obid,
isectElimination,
functionEquality,
cumulativity,
hypothesisEquality,
lambdaEquality,
functionExtensionality,
applyEquality,
hypothesis,
universeEquality,
promote_hyp,
because_Cache,
rename,
dependent_pairFormation,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
independent_functionElimination,
independent_pairFormation,
hyp_replacement,
Error :applyLambdaEquality
Latex:
\mforall{}[A,B:Type]. (A \msim{} B {}\mRightarrow{} B \msim{} A)
Date html generated:
2016_10_21-AM-10_51_56
Last ObjectModification:
2016_07_12-AM-05_55_52
Theory : equipollence!!cardinality!
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