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],
deq: EqDecider(T),
l_disjoint: l_disjoint(T;l1;l2),
l_member: (x ∈ l),
list: T List,
assert: ↑b,
uiff: uiff(P;Q),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
pi1: fst(t),
not: ¬A,
universe: Type
Lemmas :
l_member_wf,
assert_wf,
deq-member_wf,
all_wf,
not_wf,
uall_wf,
isect_wf,
list_wf,
top_wf,
deq_wf,
assert-deq-member
\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:
2015_07_17-AM-11_16_18
Last ObjectModification:
2015_01_28-AM-07_38_18
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