Nuprl Lemma : member-fpf-domain-variant
∀[A,V:Type]. ∀f:a:A fp-> V × Top. ∀eq:EqDecider(A). ∀x:A. (↑x ∈ dom(f) ⇐⇒ (x ∈ fpf-domain(f)))
Proof
Definitions occuring in Statement :
fpf-domain: fpf-domain(f),
fpf-dom: x ∈ dom(f),
fpf: a:A fp-> B[a],
deq: EqDecider(T),
l_member: (x ∈ l),
assert: ↑b,
uall: ∀[x:A]. B[x],
top: Top,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
product: x:A × B[x],
universe: Type
Lemmas :
l_member_wf,
assert-deq-member,
assert_wf,
deq-member_wf,
iff_wf,
deq_wf,
fpf_wf,
top_wf
\mforall{}[A,V:Type]. \mforall{}f:a:A fp-> V \mtimes{} Top. \mforall{}eq:EqDecider(A). \mforall{}x:A. (\muparrow{}x \mmember{} dom(f) \mLeftarrow{}{}\mRightarrow{} (x \mmember{} fpf-domain(f)))
Date html generated:
2015_07_17-AM-09_15_45
Last ObjectModification:
2015_01_28-AM-07_52_33
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