Nuprl Lemma : fpf-join-dom-sq
∀[A:Type]. ∀[eq:EqDecider(A)]. ∀[f,g:a:A fp-> Top]. ∀[x:A]. (x ∈ dom(f ⊕ g) ~ x ∈ dom(f) ∨bx ∈ 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),
bor: p ∨bq,
uall: ∀[x:A]. B[x],
top: Top,
universe: Type,
sqequal: s ~ t
Lemmas :
subtype_base_sq,
bool_wf,
bool_subtype_base,
iff_imp_equal_bool,
deq-member_wf,
append_wf,
filter_wf5,
l_member_wf,
bnot_wf,
bor_wf,
fpf_wf,
top_wf,
deq_wf,
member_filter,
assert_wf,
or_wf,
iff_wf,
member_append,
not_wf,
assert-deq-member,
iff_transitivity,
iff_weakening_uiff,
assert_of_bor,
assert_of_bnot,
equal-wf-T-base,
eqtt_to_assert,
eqff_to_assert
\mforall{}[A:Type]. \mforall{}[eq:EqDecider(A)]. \mforall{}[f,g:a:A fp-> Top]. \mforall{}[x:A].
(x \mmember{} dom(f \moplus{} g) \msim{} x \mmember{} dom(f) \mvee{}\msubb{}x \mmember{} dom(g))
Date html generated:
2015_07_17-AM-09_19_48
Last ObjectModification:
2015_01_28-AM-07_49_44
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