Nuprl Lemma : fpf-domain-join
∀[A:Type]
∀f,g:a:A fp-> Top. ∀eq:EqDecider(A). ∀x:A. ((x ∈ fpf-domain(f ⊕ g)) ⇐⇒ (x ∈ fpf-domain(f)) ∨ (x ∈ fpf-domain(g)))
Proof
Definitions occuring in Statement :
fpf-join: f ⊕ g,
fpf-domain: fpf-domain(f),
fpf: a:A fp-> B[a],
deq: EqDecider(T),
l_member: (x ∈ l),
uall: ∀[x:A]. B[x],
top: Top,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
or: P ∨ Q,
universe: Type
Lemmas :
member-fpf-domain,
fpf-join_wf,
top_wf,
deq_wf,
fpf_wf,
fpf-join-dom,
or_wf,
assert_wf,
fpf-dom_wf,
l_member_wf,
fpf-domain_wf
\mforall{}[A:Type]
\mforall{}f,g:a:A fp-> Top. \mforall{}eq:EqDecider(A). \mforall{}x:A.
((x \mmember{} fpf-domain(f \moplus{} g)) \mLeftarrow{}{}\mRightarrow{} (x \mmember{} fpf-domain(f)) \mvee{} (x \mmember{} fpf-domain(g)))
Date html generated:
2015_07_17-AM-09_19_51
Last ObjectModification:
2015_01_28-AM-07_49_08
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