Nuprl Lemma : fpf-cap-join-subtype
∀[A:Type]. ∀[eq:EqDecider(A)]. ∀[f,g:a:A fp-> Type]. ∀[a:A]. (f ⊕ g(a)?Top ⊆r f(a)?Top)
Proof
Definitions occuring in Statement :
fpf-join: f ⊕ g,
fpf-cap: f(x)?z,
fpf: a:A fp-> B[a],
deq: EqDecider(T),
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
top: Top,
universe: Type
Definitions unfolded in proof :
uall: ∀[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,
all: ∀x:A. B[x],
top: Top,
fpf-cap: f(x)?z,
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 ,
bfalse: ff,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False
Latex:
\mforall{}[A:Type]. \mforall{}[eq:EqDecider(A)]. \mforall{}[f,g:a:A fp-> Type]. \mforall{}[a:A]. (f \moplus{} g(a)?Top \msubseteq{}r f(a)?Top)
Date html generated:
2016_05_16-AM-11_31_11
Last ObjectModification:
2015_12_29-AM-09_26_53
Theory : event-ordering
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