Nuprl Lemma : latest-val-cases
∀[Info:Type]
∀es:EO+(Info)
∀[T:Type]
∀X:EClass(T). ∀e:E.
(↑e ∈b (X)- ⇐⇒ ((↑e ∈b X) ∧ ((X)-(e) = X(e) ∈ T)) ∨ (((↑e ∈b (X)') ∧ (¬↑e ∈b X)) ∧ ((X)-(e) = (X)'(e) ∈ T)))
Proof
Definitions occuring in Statement :
es-latest-val: (X)-,
es-prior-val: (X)',
eclass-val: X(e),
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
assert: ↑b,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
not: ¬A,
or: P ∨ Q,
and: P ∧ Q,
universe: Type,
equal: s = t ∈ T
Lemmas :
in-eclass_wf,
es-interface-subtype_rel2,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
top_wf,
bool_wf,
eqtt_to_assert,
bag_size_single_lemma,
bag_only_single_lemma,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
assert_of_eq_int,
bag-size_wf,
nat_wf,
single-valued-bag-if-le1,
le_weakening,
bag-only_wf2,
decidable__lt,
false_wf,
le_antisymmetry_iff,
add_functionality_wrt_le,
add-zero,
le-add-cancel,
assert_wf,
es-prior-val_wf,
not_wf,
true_wf,
eclass_wf,
or_wf,
member_wf,
eclass-val_wf,
assert_witness
Latex:
\mforall{}[Info:Type]
\mforall{}es:EO+(Info)
\mforall{}[T:Type]
\mforall{}X:EClass(T). \mforall{}e:E.
(\muparrow{}e \mmember{}\msubb{} (X)\msupminus{}
\mLeftarrow{}{}\mRightarrow{} ((\muparrow{}e \mmember{}\msubb{} X) \mwedge{} ((X)\msupminus{}(e) = X(e))) \mvee{} (((\muparrow{}e \mmember{}\msubb{} (X)') \mwedge{} (\mneg{}\muparrow{}e \mmember{}\msubb{} X)) \mwedge{} ((X)\msupminus{}(e) = (X)'(e))))
Date html generated:
2015_07_21-PM-03_22_29
Last ObjectModification:
2015_01_27-PM-06_47_56
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