Nuprl Lemma : prec_sub_wf
∀[P:Type]. ∀[a:Atom ⟶ P ⟶ ((P + P + Type) List)].
(prec_sub(P;lbl,p.a[lbl;p]) ∈ (i:P × prec(lbl,p.a[lbl;p];i)) ⟶ (i:P × prec(lbl,p.a[lbl;p];i)) ⟶ ℙ)
Proof
Definitions occuring in Statement :
prec_sub: prec_sub(P;lbl,p.a[lbl; p]),
prec: prec(lbl,p.a[lbl; p];i),
list: T List,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s1;s2],
member: t ∈ T,
function: x:A ⟶ B[x],
product: x:A × B[x],
union: left + right,
atom: Atom,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
prec_sub: prec_sub(P;lbl,p.a[lbl; p]),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Lemmas referenced :
prec-sub_wf,
istype-atom,
prec_wf,
list_wf,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
Error :lambdaEquality_alt,
spreadEquality,
hypothesisEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
applyEquality,
Error :inhabitedIsType,
hypothesis,
Error :productIsType,
Error :universeIsType,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
Error :functionIsType,
instantiate,
unionEquality,
cumulativity,
universeEquality,
Error :isect_memberEquality_alt,
Error :isectIsTypeImplies
Latex:
\mforall{}[P:Type]. \mforall{}[a:Atom {}\mrightarrow{} P {}\mrightarrow{} ((P + P + Type) List)].
(prec\_sub(P;lbl,p.a[lbl;p]) \mmember{} (i:P \mtimes{} prec(lbl,p.a[lbl;p];i))
{}\mrightarrow{} (i:P \mtimes{} prec(lbl,p.a[lbl;p];i))
{}\mrightarrow{} \mBbbP{})
Date html generated:
2019_06_20-PM-02_05_51
Last ObjectModification:
2019_02_23-PM-04_48_25
Theory : tuples
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