Nuprl Lemma : id-biject
∀[T:Type]. Bij(T;T;λx.x)
Proof
Definitions occuring in Statement :
biject: Bij(A;B;f),
uall: ∀[x:A]. B[x],
lambda: λx.A[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
biject: Bij(A;B;f),
and: P ∧ Q,
inject: Inj(A;B;f),
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
surject: Surj(A;B;f),
exists: ∃x:A. B[x]
Lemmas referenced :
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
independent_pairFormation,
lambdaFormation,
sqequalRule,
hypothesis,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
dependent_pairFormation,
because_Cache,
universeEquality
Latex:
\mforall{}[T:Type]. Bij(T;T;\mlambda{}x.x)
Date html generated:
2016_05_14-PM-01_53_56
Last ObjectModification:
2015_12_26-PM-05_40_06
Theory : list_1
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