Nuprl Lemma : fpf-const-dom
∀[A:Type]. ∀eq:EqDecider(A). ∀L:A List. ∀v:Top. ∀x:A. (↑x ∈ dom(L |-fpf-> v) ⇐⇒ (x ∈ L))
Proof
Definitions occuring in Statement :
fpf-const: L |-fpf-> v,
fpf-dom: x ∈ dom(f),
deq: EqDecider(T),
l_member: (x ∈ l),
list: T List,
assert: ↑b,
uall: ∀[x:A]. B[x],
top: Top,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
universe: Type
Lemmas :
assert-deq-member,
assert_wf,
deq-member_wf,
assert_witness,
l_member_wf,
top_wf,
list_wf,
deq_wf
\mforall{}[A:Type]. \mforall{}eq:EqDecider(A). \mforall{}L:A List. \mforall{}v:Top. \mforall{}x:A. (\muparrow{}x \mmember{} dom(L |-fpf-> v) \mLeftarrow{}{}\mRightarrow{} (x \mmember{} L))
Date html generated:
2015_07_17-AM-11_08_11
Last ObjectModification:
2015_01_28-AM-07_46_36
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