Nuprl Lemma : ptuple-monotone
∀[P:Type]. ∀[a:Atom ⟶ P ⟶ ((P + P + Type) List)]. family-monotone{i:l}(P;λX.ptuple(lbl,p.a[lbl;p];X))
Proof
Definitions occuring in Statement :
ptuple: ptuple(lbl,p.a[lbl; p];X),
list: T List,
family-monotone: family-monotone{i:l}(P;H),
uall: ∀[x:A]. B[x],
so_apply: x[s1;s2],
lambda: λx.A[x],
function: x:A ⟶ B[x],
union: left + right,
atom: Atom,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
family-monotone: family-monotone{i:l}(P;H),
all: ∀x:A. B[x],
implies: P ⇒ Q,
sub-family: F ⊆ G,
ptuple: ptuple(lbl,p.a[lbl; p];X),
prop: ℙ,
subtype_rel: A ⊆r B,
so_apply: x[s1;s2],
uimplies: b supposing a,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
sub-family_wf,
istype-atom,
list_wf,
istype-universe,
less_than_wf,
length_wf,
tuple-type_wf,
map_wf,
istype-less_than,
subtype_rel_self,
tuple-type-monotone,
subtype_rel_list,
subtype_rel_product
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
Error :lambdaFormation_alt,
sqequalRule,
because_Cache,
Error :universeIsType,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
Error :inhabitedIsType,
Error :lambdaEquality_alt,
dependent_functionElimination,
axiomEquality,
Error :functionIsTypeImplies,
Error :functionIsType,
instantiate,
unionEquality,
cumulativity,
universeEquality,
Error :isect_memberEquality_alt,
Error :isectIsTypeImplies,
setEquality,
atomEquality,
natural_numberEquality,
applyEquality,
equalityTransitivity,
equalitySymmetry,
unionElimination,
Error :equalityIstype,
independent_functionElimination,
Error :unionIsType,
setElimination,
rename,
Error :setIsType,
independent_isectElimination
Latex:
\mforall{}[P:Type]. \mforall{}[a:Atom {}\mrightarrow{} P {}\mrightarrow{} ((P + P + Type) List)].
family-monotone\{i:l\}(P;\mlambda{}X.ptuple(lbl,p.a[lbl;p];X))
Date html generated:
2019_06_20-PM-02_04_02
Last ObjectModification:
2019_02_22-PM-03_32_18
Theory : tuples
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