Nuprl Lemma : pcorec-ext
∀[P:Type]. ∀[a:Atom ⟶ P ⟶ ((P + P + Type) List)].
pcorec(lbl,p.a[lbl;p]) ≡ ptuple(lbl,p.a[lbl;p];pcorec(lbl,p.a[lbl;p]))
Proof
Definitions occuring in Statement :
pcorec: pcorec(lbl,p.a[lbl; p]),
ptuple: ptuple(lbl,p.a[lbl; p];X),
list: T List,
ext-family: F ≡ G,
uall: ∀[x:A]. B[x],
so_apply: x[s1;s2],
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],
uimplies: b supposing a,
and: P ∧ Q,
cand: A c∧ B,
ext-family: F ≡ G,
all: ∀x:A. B[x],
ext-eq: A ≡ B,
subtype_rel: A ⊆r B
Lemmas referenced :
corec-family-ext,
ptuple_wf,
istype-atom,
ptuple-continuous,
ptuple-monotone,
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,
Error :lambdaEquality_alt,
sqequalRule,
applyEquality,
Error :universeIsType,
hypothesis,
Error :functionIsType,
Error :inhabitedIsType,
independent_isectElimination,
independent_pairFormation,
because_Cache,
dependent_functionElimination,
productElimination,
independent_pairEquality,
axiomEquality,
Error :functionIsTypeImplies,
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]) \mequiv{} ptuple(lbl,p.a[lbl;p];pcorec(lbl,p.a[lbl;p]))
Date html generated:
2019_06_20-PM-02_04_07
Last ObjectModification:
2019_02_22-PM-03_29_36
Theory : tuples
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