Nuprl Lemma : equiv-bijection-property
∀A,B:Type. ∀e:{() ⊢ _:Equiv(discr(A);discr(B))}. Bij(A;B;equiv-bijection(e))
Proof
Definitions occuring in Statement :
equiv-bijection: equiv-bijection(e),
cubical-equiv: Equiv(T;A),
discrete-cubical-type: discr(T),
cubical-term: {X ⊢ _:A},
trivial-cube-set: (),
biject: Bij(A;B;f),
all: ∀x:A. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x]
Lemmas referenced :
discrete-cubical-type_wf,
cubical-equiv_wf,
trivial-cube-set_wf,
cubical-term_wf,
equiv-bijection-is_wf
Rules used in proof :
universeEquality,
hypothesis,
hypothesisEquality,
cumulativity,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
cut,
introduction,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}A,B:Type. \mforall{}e:\{() \mvdash{} \_:Equiv(discr(A);discr(B))\}. Bij(A;B;equiv-bijection(e))
Date html generated:
2017_02_21-AM-10_52_57
Last ObjectModification:
2017_02_13-PM-00_36_55
Theory : cubical!type!theory
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