Nuprl Lemma : respects-equality-list-bag
∀[A,B:Type]. respects-equality(A List;bag(B)) supposing respects-equality(A;B)
Proof
Definitions occuring in Statement :
bag: bag(T),
list: T List,
uimplies: b supposing a,
respects-equality: respects-equality(S;T),
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
respects-equality: respects-equality(S;T),
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
subtype_rel: A ⊆r B,
guard: {T}
Lemmas referenced :
list-subtype-bag,
equal_functionality_wrt_subtype_rel2,
list_wf,
bag_wf,
respects-equality-bag,
change-equality-type,
istype-base,
respects-equality_wf,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
lambdaFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
because_Cache,
independent_isectElimination,
lambdaEquality_alt,
universeIsType,
hypothesis,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
dependent_functionElimination,
sqequalRule,
equalityIstype,
sqequalBase,
inhabitedIsType,
instantiate,
universeEquality
Latex:
\mforall{}[A,B:Type]. respects-equality(A List;bag(B)) supposing respects-equality(A;B)
Date html generated:
2019_10_15-AM-10_59_51
Last ObjectModification:
2018_12_03-PM-00_13_17
Theory : bags
Home
Index