Nuprl Lemma : accum-class_wf
∀[Info,A,B:Type]. ∀[X:EClass(A)]. ∀[b:A ⟶ B]. ∀[f:B ⟶ A ⟶ B]. (accum-class(b,a.f[b;a];a.b[a];X) ∈ EClass(B))
Proof
Definitions occuring in Statement :
accum-class: accum-class(a,x.f[a; x];x.base[x];X),
eclass: EClass(A[eo; e]),
uall: ∀[x:A]. B[x],
so_apply: x[s1;s2],
so_apply: x[s],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
accum-class: accum-class(a,x.f[a; x];x.base[x];X),
eclass: EClass(A[eo; e]),
subtype_rel: A ⊆r B,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
uimplies: b supposing a,
all: ∀x:A. B[x],
top: Top,
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
and: P ∧ Q,
es-E-interface: E(X),
so_lambda: λ2x.t[x],
so_apply: x[s],
sq_type: SQType(T),
guard: {T},
assert: ↑b,
true: True,
prop: ℙ,
bfalse: ff,
exists: ∃x:A. B[x],
or: P ∨ Q,
bnot: ¬bb,
false: False
Latex:
\mforall{}[Info,A,B:Type]. \mforall{}[X:EClass(A)]. \mforall{}[b:A {}\mrightarrow{} B]. \mforall{}[f:B {}\mrightarrow{} A {}\mrightarrow{} B].
(accum-class(b,a.f[b;a];a.b[a];X) \mmember{} EClass(B))
Date html generated:
2016_05_16-PM-11_09_09
Last ObjectModification:
2015_12_29-AM-10_35_40
Theory : event-ordering
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