Nuprl Lemma : fpf-compatible-join-cap
∀[A:Type]. ∀[eq:EqDecider(A)]. ∀[B:A ⟶ Type]. ∀[f,g:a:A fp-> B[a]]. ∀[x:A]. ∀[z:B[x]].
f ⊕ g(x)?z = g(x)?f(x)?z ∈ B[x] supposing f || g
Proof
Definitions occuring in Statement :
fpf-join: f ⊕ g,
fpf-compatible: f || g,
fpf-cap: f(x)?z,
fpf: a:A fp-> B[a],
deq: EqDecider(T),
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-compatible: f || g,
fpf-cap: f(x)?z,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
top: Top,
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
guard: {T},
rev_implies: P ⇐ Q,
not: ¬A,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
bfalse: ff,
cand: A c∧ B,
or: P ∨ Q,
false: False
Latex:
\mforall{}[A:Type]. \mforall{}[eq:EqDecider(A)]. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[f,g:a:A fp-> B[a]]. \mforall{}[x:A]. \mforall{}[z:B[x]].
f \moplus{} g(x)?z = g(x)?f(x)?z supposing f || g
Date html generated:
2016_05_16-AM-11_30_47
Last ObjectModification:
2015_12_29-AM-09_27_31
Theory : event-ordering
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