Nuprl Lemma : compact_functionality_wrt_equipollent
∀[T,S:Type]. (T ~ S ⇒ compact-type(T) ⇒ compact-type(S))
Proof
Definitions occuring in Statement :
compact-type: compact-type(T),
equipollent: A ~ B,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
implies: P ⇒ Q,
equipollent: A ~ B,
exists: ∃x:A. B[x],
biject: Bij(A;B;f),
and: P ∧ Q,
prop: ℙ
Lemmas referenced :
compact_functionality_wrt_surject,
surject_wf,
equipollent_wf
Rules used in proof :
cut,
lemma_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
lambdaFormation,
independent_functionElimination,
productElimination,
dependent_pairFormation,
because_Cache,
universeEquality
Latex:
\mforall{}[T,S:Type]. (T \msim{} S {}\mRightarrow{} compact-type(T) {}\mRightarrow{} compact-type(S))
Date html generated:
2016_05_15-PM-01_46_28
Last ObjectModification:
2015_12_27-AM-00_09_54
Theory : basic
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