Nuprl Lemma : member-p-union
∀p:FinProbSpace. ∀A,B:p-open(p). ∀s:ℕ ─→ Outcome. (s ∈ p-union(A;B) ⇐⇒ s ∈ A ∨ s ∈ B)
Proof
Definitions occuring in Statement :
p-union: p-union(A;B),
p-open-member: s ∈ C,
p-open: p-open(p),
p-outcome: Outcome,
finite-prob-space: FinProbSpace,
nat: ℕ,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
or: P ∨ Q,
function: x:A ─→ B[x]
Lemmas :
exists_wf,
nat_wf,
equal-wf-T-base,
eq_int_wf,
subtype_rel_dep_function,
p-outcome_wf,
int_seg_wf,
int_seg_subtype-nat,
false_wf,
subtype_rel_self,
bool_wf,
eqtt_to_assert,
assert_of_eq_int,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
or_wf,
set_wf,
all_wf,
le_wf,
finite-prob-space_wf,
assert_wf,
bnot_wf,
not_wf,
bool_cases,
iff_transitivity,
iff_weakening_uiff,
assert_of_bnot,
int_subtype_base,
uiff_transitivity
\mforall{}p:FinProbSpace. \mforall{}A,B:p-open(p). \mforall{}s:\mBbbN{} {}\mrightarrow{} Outcome. (s \mmember{} p-union(A;B) \mLeftarrow{}{}\mRightarrow{} s \mmember{} A \mvee{} s \mmember{} B)
Date html generated:
2015_07_17-AM-08_00_29
Last ObjectModification:
2015_01_27-AM-11_22_23
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