Nuprl Lemma : subtype-fpf-cap-top2
∀[X,T:Type]. ∀[eq:EqDecider(X)]. ∀[g:x:X fp-> Type]. ∀[x:X]. T ⊆r g(x)?Top supposing (↑x ∈ dom(g)) ⇒ (T ⊆r g(x))
Proof
Definitions occuring in Statement :
fpf-cap: f(x)?z,
fpf-ap: f(x),
fpf-dom: x ∈ dom(f),
fpf: a:A fp-> B[a],
deq: EqDecider(T),
assert: ↑b,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
top: Top,
implies: P ⇒ Q,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
fpf-cap: f(x)?z,
subtype_rel: A ⊆r B,
implies: P ⇒ Q,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
top: Top,
all: ∀x:A. B[x],
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{}[X,T:Type]. \mforall{}[eq:EqDecider(X)]. \mforall{}[g:x:X fp-> Type]. \mforall{}[x:X].
T \msubseteq{}r g(x)?Top supposing (\muparrow{}x \mmember{} dom(g)) {}\mRightarrow{} (T \msubseteq{}r g(x))
Date html generated:
2016_05_16-AM-11_07_34
Last ObjectModification:
2015_12_29-AM-09_15_32
Theory : event-ordering
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