Nuprl Lemma : pcorec_wf
∀[P:Type]. ∀[a:Atom ⟶ P ⟶ ((P + P + Type) List)]. (pcorec(lbl,p.a[lbl;p]) ∈ P ⟶ Type)
Proof
Definitions occuring in Statement :
pcorec: pcorec(lbl,p.a[lbl; p]),
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,
pcorec: pcorec(lbl,p.a[lbl; p]),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Lemmas referenced :
corec-family_wf,
ptuple_wf,
istype-atom,
list_wf,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
Error :lambdaEquality_alt,
applyEquality,
Error :universeIsType,
hypothesis,
Error :functionIsType,
Error :inhabitedIsType,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
instantiate,
unionEquality,
cumulativity,
universeEquality,
Error :isect_memberEquality_alt,
Error :isectIsTypeImplies
Latex:
\mforall{}[P:Type]. \mforall{}[a:Atom {}\mrightarrow{} P {}\mrightarrow{} ((P + P + Type) List)]. (pcorec(lbl,p.a[lbl;p]) \mmember{} P {}\mrightarrow{} Type)
Date html generated:
2019_06_20-PM-02_04_05
Last ObjectModification:
2019_02_22-PM-03_29_12
Theory : tuples
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