Nuprl Lemma : fpf-join-empty
∀[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,
append: as @ bs,
so_lambda: so_lambda(x,y,z.t[x; y; z]),
so_apply: x[s1;s2;s3],
fpf-cap: f(x)?z,
fpf-dom: x ∈ dom(f),
bnot: ¬bb,
ifthenelse: if b then t else f fi ,
bfalse: ff,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
prop: ℙ,
so_apply: x[s],
uimplies: b supposing a,
implies: P ⇒ Q,
iff: P ⇐⇒ Q,
and: P ∧ Q,
assert: ↑b,
btrue: tt
Latex:
\mforall{}[A:Type]. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[f:a:A fp-> B[a]]. \mforall{}[eq:EqDecider(A)]. (\motimes{} \moplus{} f = f)
Date html generated:
2016_05_16-AM-11_09_39
Last ObjectModification:
2015_12_29-AM-09_16_51
Theory : event-ordering
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