Nuprl Lemma : colist-unfold_wf
∀[A,B:Type]. ∀[P:B ⟶ (Unit + (A × B))]. ∀[x:B]. (colist-unfold(P;x) ∈ colist(A))
Proof
Definitions occuring in Statement :
colist-unfold: colist-unfold(P;x),
colist: colist(T),
uall: ∀[x:A]. B[x],
unit: Unit,
member: t ∈ T,
function: x:A ⟶ B[x],
product: x:A × B[x],
union: left + right,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
colist-unfold: colist-unfold(P;x),
colist: colist(T),
so_lambda: λ2x.t[x],
so_apply: x[s],
cons: [a / b],
nil: [],
isect2: T1 ⋂ T2,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
top: Top,
bfalse: ff,
all: ∀x:A. B[x],
implies: P ⇒ Q,
subtype_rel: A ⊆r B,
prop: ℙ
Lemmas referenced :
unit_wf2,
fix_wf_corec_parameter,
b-union_wf,
top_wf,
it_wf,
subtype_rel_b-union-left,
subtype_rel_b-union-right,
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
sqequalHypSubstitution,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
hypothesisEquality,
isect_memberEquality,
isectElimination,
thin,
because_Cache,
functionEquality,
cumulativity,
unionEquality,
extract_by_obid,
productEquality,
universeEquality,
lambdaEquality,
unionElimination,
equalityElimination,
functionExtensionality,
voidElimination,
voidEquality,
lambdaFormation,
applyEquality,
productElimination,
independent_pairEquality,
dependent_functionElimination,
independent_functionElimination
Latex:
\mforall{}[A,B:Type]. \mforall{}[P:B {}\mrightarrow{} (Unit + (A \mtimes{} B))]. \mforall{}[x:B]. (colist-unfold(P;x) \mmember{} colist(A))
Date html generated:
2018_05_21-PM-10_20_24
Last ObjectModification:
2017_07_26-PM-06_37_26
Theory : eval!all
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