Nuprl Lemma : fpf-union-contains
∀[A:Type]. ∀[B:A ⟶ Type].
∀eq:EqDecider(A). ∀f,g:x:A fp-> B[x] List. ∀x:A. ∀R:⋂a:A. ((B[a] List) ⟶ B[a] ⟶ 𝔹). f(x)?[] ⊆ fpf-union(f;g;eq;R;x)
Proof
Definitions occuring in Statement :
fpf-union: fpf-union(f;g;eq;R;x),
fpf-cap: f(x)?z,
fpf: a:A fp-> B[a],
l_contains: A ⊆ B,
nil: [],
list: T List,
deq: EqDecider(T),
bool: 𝔹,
uall: ∀[x:A]. B[x],
so_apply: x[s],
all: ∀x:A. B[x],
isect: ⋂x:A. B[x],
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
fpf-union: fpf-union(f;g;eq;R;x),
fpf-cap: f(x)?z,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
top: Top,
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
ifthenelse: if b then t else f fi ,
band: p ∧b q,
prop: ℙ,
bfalse: ff,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False
Latex:
\mforall{}[A:Type]. \mforall{}[B:A {}\mrightarrow{} Type].
\mforall{}eq:EqDecider(A). \mforall{}f,g:x:A fp-> B[x] List. \mforall{}x:A. \mforall{}R:\mcap{}a:A. ((B[a] List) {}\mrightarrow{} B[a] {}\mrightarrow{} \mBbbB{}).
f(x)?[] \msubseteq{} fpf-union(f;g;eq;R;x)
Date html generated:
2016_05_16-AM-11_05_22
Last ObjectModification:
2015_12_29-AM-09_13_51
Theory : event-ordering
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