Nuprl Lemma : l_disjoint-fpf-dom
∀[A:Type]. ∀[eq:EqDecider(A)]. ∀[f:a:A fp-> Top]. ∀[L:A List].
uiff(l_disjoint(A;fst(f);L);∀[a:A]. ¬(a ∈ L) supposing ↑a ∈ dom(f))
Proof
Definitions occuring in Statement :
fpf-dom: x ∈ dom(f),
fpf: a:A fp-> B[a],
l_disjoint: l_disjoint(T;l1;l2),
l_member: (x ∈ l),
list: T List,
deq: EqDecider(T),
assert: ↑b,
uiff: uiff(P;Q),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
pi1: fst(t),
not: ¬A,
universe: Type
Definitions unfolded in proof :
fpf-dom: x ∈ dom(f),
l_disjoint: l_disjoint(T;l1;l2),
fpf: a:A fp-> B[a],
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
not: ¬A,
implies: P ⇒ Q,
false: False,
prop: ℙ,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
all: ∀x:A. B[x],
top: Top,
iff: P ⇐⇒ Q,
cand: A c∧ B,
rev_implies: P ⇐ Q
Latex:
\mforall{}[A:Type]. \mforall{}[eq:EqDecider(A)]. \mforall{}[f:a:A fp-> Top]. \mforall{}[L:A List].
uiff(l\_disjoint(A;fst(f);L);\mforall{}[a:A]. \mneg{}(a \mmember{} L) supposing \muparrow{}a \mmember{} dom(f))
Date html generated:
2016_05_16-AM-11_36_21
Last ObjectModification:
2015_12_29-AM-09_31_11
Theory : event-ordering
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