Nuprl Lemma : subtype-fpf-cap-void2
∀[X:Type]. ∀[eq:EqDecider(X)]. ∀[f,g:x:X fp-> Type]. ∀[x:X]. ∀[z:g(x)?Void]. f(x)?Void ⊆r g(x)?Void supposing f || g
Proof
Definitions occuring in Statement :
fpf-compatible: f || g,
fpf-cap: f(x)?z,
fpf: a:A fp-> B[a],
deq: EqDecider(T),
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
void: Void,
universe: Type
Definitions unfolded in proof :
member: t ∈ T,
uall: ∀[x:A]. B[x],
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-compatible: f || g,
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,
prop: ℙ,
cand: A c∧ B,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
or: P ∨ Q,
sq_type: SQType(T),
not: ¬A,
false: False
Latex:
\mforall{}[X:Type]. \mforall{}[eq:EqDecider(X)]. \mforall{}[f,g:x:X fp-> Type]. \mforall{}[x:X]. \mforall{}[z:g(x)?Void].
f(x)?Void \msubseteq{}r g(x)?Void supposing f || g
Date html generated:
2016_05_16-AM-11_09_05
Last ObjectModification:
2015_12_29-AM-09_16_28
Theory : event-ordering
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