Nuprl Lemma : fpf-single-dom
∀[A:Type]. ∀[eq:EqDecider(A)]. ∀[x,y:A]. ∀[v:Top]. uiff(↑x ∈ dom(y : v);x = y ∈ A)
Proof
Definitions occuring in Statement :
fpf-single: x : v,
fpf-dom: x ∈ dom(f),
deq: EqDecider(T),
assert: ↑b,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
top: Top,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
member: t ∈ T,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
so_apply: x[s],
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
prop: ℙ,
implies: P ⇒ Q,
or: P ∨ Q,
fpf-single: x : v,
fpf-dom: x ∈ dom(f),
pi1: fst(t),
all: ∀x:A. B[x],
top: Top,
iff: P ⇐⇒ Q,
assert: ↑b,
ifthenelse: if b then t else f fi ,
bfalse: ff,
rev_implies: P ⇐ Q,
eqof: eqof(d),
false: False
Latex:
\mforall{}[A:Type]. \mforall{}[eq:EqDecider(A)]. \mforall{}[x,y:A]. \mforall{}[v:Top]. uiff(\muparrow{}x \mmember{} dom(y : v);x = y)
Date html generated:
2016_05_16-AM-11_29_31
Last ObjectModification:
2015_12_29-AM-09_25_28
Theory : event-ordering
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