Nuprl Lemma : alist-map_wf
∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[L:(T × T) List]. (alist-map(eq;L) ∈ T ⟶ T)
Proof
Definitions occuring in Statement :
alist-map: alist-map(eq;L),
list: T List,
deq: EqDecider(T),
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
product: x:A × B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
alist-map: alist-map(eq;L),
all: ∀x:A. B[x],
implies: P ⇒ Q
Lemmas referenced :
apply-alist_wf,
list_wf,
deq_wf,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
lambdaEquality_alt,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
inhabitedIsType,
lambdaFormation_alt,
unionElimination,
equalityIstype,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
independent_functionElimination,
universeIsType,
axiomEquality,
productEquality,
isect_memberEquality_alt,
isectIsTypeImplies,
instantiate,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[eq:EqDecider(T)]. \mforall{}[L:(T \mtimes{} T) List]. (alist-map(eq;L) \mmember{} T {}\mrightarrow{} T)
Date html generated:
2020_05_19-PM-09_51_04
Last ObjectModification:
2020_01_26-PM-10_27_43
Theory : list_1
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