Nuprl Lemma : prec_wf
∀[P:Type]. ∀[a:Atom ⟶ P ⟶ ((P + P + Type) List)]. ∀[i:P]. (prec(lbl,p.a[lbl;p];i) ∈ Type)
Proof
Definitions occuring in Statement :
prec: prec(lbl,p.a[lbl; p];i),
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: prec(lbl,p.a[lbl; p];i),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
uimplies: b supposing a,
nat: ℕ,
so_lambda: λ2x.t[x],
so_apply: x[s],
prop: ℙ
Lemmas referenced :
pcorec_wf,
has-value_wf-partial,
nat_wf,
set-value-type,
le_wf,
istype-int,
int-value-type,
pcorec-size_wf,
istype-atom,
list_wf,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
setEquality,
applyEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
Error :lambdaEquality_alt,
because_Cache,
hypothesis,
independent_isectElimination,
intEquality,
natural_numberEquality,
Error :inhabitedIsType,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
Error :universeIsType,
Error :isect_memberEquality_alt,
Error :isectIsTypeImplies,
Error :functionIsType,
instantiate,
unionEquality,
cumulativity,
universeEquality
Latex:
\mforall{}[P:Type]. \mforall{}[a:Atom {}\mrightarrow{} P {}\mrightarrow{} ((P + P + Type) List)]. \mforall{}[i:P]. (prec(lbl,p.a[lbl;p];i) \mmember{} Type)
Date html generated:
2019_06_20-PM-02_04_21
Last ObjectModification:
2019_02_28-PM-02_06_35
Theory : tuples
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