Nuprl Lemma : fpf-join-dom
∀[A:Type]. ∀[B:A ─→ Type].
∀eq:EqDecider(A). ∀f,g:a:A fp-> B[a]. ∀x:A. (↑x ∈ dom(f ⊕ g) ⇐⇒ (↑x ∈ dom(f)) ∨ (↑x ∈ dom(g)))
Proof
Definitions occuring in Statement :
fpf-join: f ⊕ g,
fpf-dom: x ∈ dom(f),
fpf: a:A fp-> B[a],
deq: EqDecider(T),
assert: ↑b,
uall: ∀[x:A]. B[x],
so_apply: x[s],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
or: P ∨ Q,
function: x:A ─→ B[x],
universe: Type
Lemmas :
deq-member_wf,
bool_wf,
eqtt_to_assert,
assert-deq-member,
l_member_wf,
or_wf,
false_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
true_wf,
member_filter,
bnot_wf,
assert_wf,
filter_wf5,
iff_wf,
member_append,
append_wf,
list_wf,
deq_wf
\mforall{}[A:Type]. \mforall{}[B:A {}\mrightarrow{} Type].
\mforall{}eq:EqDecider(A). \mforall{}f,g:a:A fp-> B[a]. \mforall{}x:A. (\muparrow{}x \mmember{} dom(f \moplus{} g) \mLeftarrow{}{}\mRightarrow{} (\muparrow{}x \mmember{} dom(f)) \mvee{} (\muparrow{}x \mmember{} dom(g)))
Date html generated:
2015_07_17-AM-09_19_40
Last ObjectModification:
2015_01_28-AM-07_49_56
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