Nuprl Lemma : ptuple_wf
∀[P:Type]. ∀[a:Atom ⟶ P ⟶ ((P + P + Type) List)]. ∀[X:P ⟶ Type]. (ptuple(lbl,p.a[lbl;p];X) ∈ P ⟶ Type)
Proof
Definitions occuring in Statement :
ptuple: ptuple(lbl,p.a[lbl; p];X),
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,
ptuple: ptuple(lbl,p.a[lbl; p];X),
so_apply: x[s1;s2],
prop: ℙ,
all: ∀x:A. B[x],
implies: P ⇒ Q
Lemmas referenced :
less_than_wf,
length_wf,
tuple-type_wf,
map_wf,
list_wf,
istype-atom,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
Error :lambdaEquality_alt,
productEquality,
setEquality,
atomEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
instantiate,
unionEquality,
cumulativity,
hypothesisEquality,
universeEquality,
applyEquality,
hypothesis,
equalityTransitivity,
equalitySymmetry,
Error :inhabitedIsType,
Error :lambdaFormation_alt,
unionElimination,
Error :equalityIstype,
dependent_functionElimination,
independent_functionElimination,
Error :unionIsType,
setElimination,
rename,
Error :universeIsType,
axiomEquality,
Error :functionIsType,
Error :isect_memberEquality_alt,
Error :isectIsTypeImplies
Latex:
\mforall{}[P:Type]. \mforall{}[a:Atom {}\mrightarrow{} P {}\mrightarrow{} ((P + P + Type) List)]. \mforall{}[X:P {}\mrightarrow{} Type].
(ptuple(lbl,p.a[lbl;p];X) \mmember{} P {}\mrightarrow{} Type)
Date html generated:
2019_06_20-PM-02_03_50
Last ObjectModification:
2019_02_22-PM-03_13_30
Theory : tuples
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