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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