Nuprl Lemma : ext-eq-implies-biject
∀[T,S:Type]. (T ≡ S ⇒ Bij(S;T;λx.x))
Proof
Definitions occuring in Statement :
biject: Bij(A;B;f),
ext-eq: A ≡ B,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
lambda: λx.A[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
biject: Bij(A;B;f),
and: P ∧ Q,
inject: Inj(A;B;f),
all: ∀x:A. B[x],
guard: {T},
uimplies: b supposing a,
subtype_rel: A ⊆r B,
surject: Surj(A;B;f),
exists: ∃x:A. B[x]
Lemmas referenced :
ext-eq_wf,
subtype_rel_weakening,
equal_functionality_wrt_subtype_rel2,
equal_wf,
ext-eq_inversion
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
hypothesis,
universeEquality,
independent_pairFormation,
sqequalRule,
independent_isectElimination,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
applyEquality,
dependent_pairFormation
Latex:
\mforall{}[T,S:Type]. (T \mequiv{} S {}\mRightarrow{} Bij(S;T;\mlambda{}x.x))
Date html generated:
2016_10_21-AM-09_40_40
Last ObjectModification:
2016_08_07-PM-06_29_39
Theory : fun_1
Home
Index