Nuprl Lemma : fpf-join-ap-left
∀[A:Type]. ∀[B,C:A ⟶ Type]. ∀[eq:EqDecider(A)]. ∀[f:a:A fp-> B[a]]. ∀[g:a:A fp-> C[a]]. ∀[x:A].
f ⊕ g(x) = f(x) ∈ B[x] supposing ↑x ∈ dom(f)
Proof
Definitions occuring in Statement :
fpf-join: f ⊕ g,
fpf-ap: f(x),
fpf-dom: x ∈ dom(f),
fpf: a:A fp-> B[a],
deq: EqDecider(T),
assert: ↑b,
uimplies: b supposing a,
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,
uimplies: b supposing a,
fpf-ap: f(x),
fpf-join: f ⊕ g,
pi2: snd(t),
fpf-cap: f(x)?z,
prop: ℙ,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
all: ∀x:A. B[x],
top: Top,
not: ¬A,
implies: P ⇒ Q,
false: False,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
ifthenelse: if b then t else f fi ,
bfalse: ff
Latex:
\mforall{}[A:Type]. \mforall{}[B,C:A {}\mrightarrow{} Type]. \mforall{}[eq:EqDecider(A)]. \mforall{}[f:a:A fp-> B[a]]. \mforall{}[g:a:A fp-> C[a]]. \mforall{}[x:A].
f \moplus{} g(x) = f(x) supposing \muparrow{}x \mmember{} dom(f)
Date html generated:
2016_05_16-AM-11_11_08
Last ObjectModification:
2015_12_29-AM-09_17_45
Theory : event-ordering
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