Nuprl Lemma : fpf-empty-join
∀[A:Type]. ∀[B:A ⟶ Type]. ∀[f:a:A fp-> B[a]]. ∀[eq:EqDecider(A)]. (f ⊕ ⊗ = f ∈ a:A fp-> B[a])
Proof
Definitions occuring in Statement :
fpf-join: f ⊕ g,
fpf-empty: ⊗,
fpf: a:A fp-> B[a],
deq: EqDecider(T),
uall: ∀[x:A]. B[x],
so_apply: x[s],
function: x:A ⟶ B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
fpf: a:A fp-> B[a],
fpf-empty: ⊗,
fpf-join: f ⊕ g,
pi1: fst(t),
all: ∀x:A. B[x],
top: Top,
fpf-cap: f(x)?z,
fpf-dom: x ∈ dom(f),
subtype_rel: A ⊆r B,
uimplies: b supposing a,
prop: ℙ,
so_apply: x[s],
so_lambda: λ2x.t[x],
not: ¬A,
implies: P ⇒ Q,
false: False,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
ifthenelse: if b then t else f fi ,
bfalse: ff
Latex:
\mforall{}[A:Type]. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[f:a:A fp-> B[a]]. \mforall{}[eq:EqDecider(A)]. (f \moplus{} \motimes{} = f)
Date html generated:
2016_05_16-AM-11_09_43
Last ObjectModification:
2015_12_29-AM-09_22_33
Theory : event-ordering
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