Nuprl Lemma : prec-arg-types_wf
∀[P:Type]. ∀[a:Atom ⟶ P ⟶ ((P + P + Type) List)]. ∀[i:P]. ∀[lbl:Atom].
(prec-arg-types(lbl,p.a[lbl;p];i;lbl) ∈ Type List)
Proof
Definitions occuring in Statement :
prec-arg-types: prec-arg-types(lbl,p.a[lbl; p];i;lbl),
list: T List,
uall: ∀[x:A]. B[x],
so_apply: x[s1;s2],
member: t ∈ T,
function: x:A ⟶ B[x],
union: left + right,
atom: Atom,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
prec-arg-types: prec-arg-types(lbl,p.a[lbl; p];i;lbl),
all: ∀x:A. B[x],
implies: P ⇒ Q,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Lemmas referenced :
map_wf,
prec_wf,
list_wf,
istype-atom,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
thin,
instantiate,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
unionEquality,
cumulativity,
hypothesisEquality,
universeEquality,
Error :lambdaEquality_alt,
equalityTransitivity,
hypothesis,
equalitySymmetry,
Error :inhabitedIsType,
Error :lambdaFormation_alt,
unionElimination,
applyEquality,
Error :equalityIstype,
dependent_functionElimination,
independent_functionElimination,
Error :unionIsType,
axiomEquality,
Error :isect_memberEquality_alt,
Error :isectIsTypeImplies,
Error :universeIsType,
Error :functionIsType
Latex:
\mforall{}[P:Type]. \mforall{}[a:Atom {}\mrightarrow{} P {}\mrightarrow{} ((P + P + Type) List)]. \mforall{}[i:P]. \mforall{}[lbl:Atom].
(prec-arg-types(lbl,p.a[lbl;p];i;lbl) \mmember{} Type List)
Date html generated:
2019_06_20-PM-02_05_11
Last ObjectModification:
2019_02_22-PM-06_23_46
Theory : tuples
Home
Index