Nuprl Lemma : fpf-domain-union-join
∀[A:Type]
∀f:a:A fp-> Top List. ∀g:a:A fp-> Top. ∀eq:EqDecider(A). ∀x:A. ∀R:Top.
((x ∈ fpf-domain(fpf-union-join(eq;R;f;g))) ⇐⇒ (x ∈ fpf-domain(f)) ∨ (x ∈ fpf-domain(g)))
Proof
Definitions occuring in Statement :
fpf-union-join: fpf-union-join(eq;R;f;g),
fpf-domain: fpf-domain(f),
fpf: a:A fp-> B[a],
deq: EqDecider(T),
l_member: (x ∈ l),
list: T List,
uall: ∀[x:A]. B[x],
top: Top,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
or: P ∨ Q,
universe: Type
Lemmas :
or_wf,
l_member_wf,
assert_wf,
bnot_wf,
deq-member_wf,
decidable__assert,
assert-deq-member,
member_filter,
filter_wf5,
iff_wf,
member_append,
append_wf,
top_wf,
deq_wf,
fpf_wf,
list_wf,
not_wf,
iff_transitivity,
iff_weakening_uiff,
assert_of_bnot
\mforall{}[A:Type]
\mforall{}f:a:A fp-> Top List. \mforall{}g:a:A fp-> Top. \mforall{}eq:EqDecider(A). \mforall{}x:A. \mforall{}R:Top.
((x \mmember{} fpf-domain(fpf-union-join(eq;R;f;g))) \mLeftarrow{}{}\mRightarrow{} (x \mmember{} fpf-domain(f)) \mvee{} (x \mmember{} fpf-domain(g)))
Date html generated:
2015_07_17-AM-09_21_44
Last ObjectModification:
2015_01_28-AM-07_47_14
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