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),
l_member: (x ∈ l),
list: T List,
deq: EqDecider(T),
assert: ↑b,
uall: ∀[x:A]. B[x],
top: Top,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
universe: Type
Definitions unfolded in proof :
fpf-const: L |-fpf-> v,
fpf-dom: x ∈ dom(f),
pi1: fst(t),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
rev_implies: P ⇐ Q
Latex:
\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:
2016_05_16-AM-11_15_38
Last ObjectModification:
2015_12_29-AM-09_20_06
Theory : event-ordering
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