### Nuprl Lemma : pcorec-size_wf

`∀[P:Type]. ∀[a:Atom ⟶ P ⟶ ((P + P + Type) List)].`
`  (pcorec-size(lbl,p.a[lbl;p]) ∈ i:P ⟶ (pcorec(lbl,p.a[lbl;p]) i) ⟶ partial(ℕ))`

Proof

Definitions occuring in Statement :  pcorec-size: `pcorec-size(lbl,p.a[lbl; p])` pcorec: `pcorec(lbl,p.a[lbl; p])` list: `T List` partial: `partial(T)` nat: `ℕ` uall: `∀[x:A]. B[x]` so_apply: `x[s1;s2]` member: `t ∈ T` apply: `f a` 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-size: `pcorec-size(lbl,p.a[lbl; p])` so_lambda: `λ2x y.t[x; y]` so_apply: `x[s1;s2]` ptuple: `ptuple(lbl,p.a[lbl; p];X)` nat: `ℕ` le: `A ≤ B` and: `P ∧ Q` less_than': `less_than'(a;b)` false: `False` not: `¬A` implies: `P `` Q`
Lemmas referenced :  fix_wf-pcorec-partial-nat add-wf-partial-nat nat-partial-nat istype-false istype-le add-sz_wf ptuple_wf istype-atom partial_wf nat_wf list_wf istype-universe
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity Error :isect_memberFormation_alt,  introduction cut extract_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality sqequalRule Error :lambdaEquality_alt,  applyEquality Error :universeIsType,  because_Cache Error :isect_memberEquality_alt,  productElimination Error :dependent_set_memberEquality_alt,  natural_numberEquality independent_pairFormation Error :lambdaFormation_alt,  hypothesis setElimination rename Error :inhabitedIsType,  Error :functionIsType,  axiomEquality equalityTransitivity equalitySymmetry instantiate unionEquality cumulativity universeEquality Error :isectIsTypeImplies

Latex:
\mforall{}[P:Type].  \mforall{}[a:Atom  {}\mrightarrow{}  P  {}\mrightarrow{}  ((P  +  P  +  Type)  List)].
(pcorec-size(lbl,p.a[lbl;p])  \mmember{}  i:P  {}\mrightarrow{}  (pcorec(lbl,p.a[lbl;p])  i)  {}\mrightarrow{}  partial(\mBbbN{}))

Date html generated: 2019_06_20-PM-02_04_16
Last ObjectModification: 2019_02_22-PM-03_32_14

Theory : tuples

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