### 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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