Nuprl Lemma : mk-prec_wf
∀[P:Type]. ∀[a:Atom ⟶ P ⟶ ((P + P + Type) List)]. ∀[i:P]. ∀[labl:{lbl:Atom| 0 < ||a[lbl;i]||} ].
∀[x:tuple-type(prec-arg-types(lbl,p.a[lbl;p];i;labl))].
(mk-prec(labl;x) ∈ prec(lbl,p.a[lbl;p];i))
Proof
Definitions occuring in Statement :
mk-prec: mk-prec(lbl;x),
prec-arg-types: prec-arg-types(lbl,p.a[lbl; p];i;lbl),
prec: prec(lbl,p.a[lbl; p];i),
tuple-type: tuple-type(L),
length: ||as||,
list: T List,
less_than: a < b,
uall: ∀[x:A]. B[x],
so_apply: x[s1;s2],
member: t ∈ T,
set: {x:A| B[x]} ,
function: x:A ⟶ B[x],
union: left + right,
natural_number: $n,
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),
mk-prec: mk-prec(lbl;x),
so_apply: x[s1;s2],
all: ∀x:A. B[x],
implies: P ⇒ Q,
so_lambda: λ2x y.t[x; y],
subtype_rel: A ⊆r B,
ext-eq: A ≡ B,
and: P ∧ Q
Lemmas referenced :
prec-ext,
istype-less_than,
length_wf,
tuple-type_wf,
map_wf,
prec_wf,
list_wf,
prec-arg-types_wf,
istype-atom,
istype-universe
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
setElimination,
rename,
sqequalRule,
Error :dependent_pairEquality_alt,
Error :dependent_set_memberEquality_alt,
natural_numberEquality,
instantiate,
unionEquality,
cumulativity,
universeEquality,
applyEquality,
Error :universeIsType,
Error :lambdaEquality_alt,
equalityTransitivity,
equalitySymmetry,
Error :inhabitedIsType,
Error :lambdaFormation_alt,
unionElimination,
Error :equalityIstype,
dependent_functionElimination,
independent_functionElimination,
Error :unionIsType,
Error :setIsType,
Error :functionIsType,
productElimination
Latex:
\mforall{}[P:Type]. \mforall{}[a:Atom {}\mrightarrow{} P {}\mrightarrow{} ((P + P + Type) List)]. \mforall{}[i:P]. \mforall{}[labl:\{lbl:Atom| 0 < ||a[lbl;i]||\} ].
\mforall{}[x:tuple-type(prec-arg-types(lbl,p.a[lbl;p];i;labl))].
(mk-prec(labl;x) \mmember{} prec(lbl,p.a[lbl;p];i))
Date html generated:
2019_06_20-PM-02_05_14
Last ObjectModification:
2019_02_22-PM-06_26_11
Theory : tuples
Home
Index