Nuprl Lemma : prior-or-latest
∀[Info,A,B:Type]. ∀[X:EClass(A)]. ∀[Y:EClass(B)].
((X |- Y))' = ((X)' | (Y)') ∈ EClass(one_or_both(A;B)) supposing Singlevalued(X) ∧ Singlevalued(Y)
Proof
Definitions occuring in Statement :
es-or-latest: (X |- Y),
es-prior-val: (X)',
es-interface-or: (X | Y),
sv-class: Singlevalued(X),
eclass: EClass(A[eo; e]),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
and: P ∧ Q,
universe: Type,
equal: s = t ∈ T,
one_or_both: one_or_both(A;B)
Lemmas :
es-locl_wf,
assert_wf,
in-eclass_wf,
exists_wf,
es-E_wf,
event-ordering+_subtype,
or_wf,
es-interface-subtype_rel2,
top_wf,
is-prior-val,
one_or_both_wf,
es-or-latest_wf,
is-or-latest,
subtype_top,
es-prior-val_wf,
is-interface-or,
es-interface-or_wf,
all_wf,
iff_wf,
sv-class_wf,
event-ordering+_wf,
eclass_wf,
es-interface-extensionality,
bool_wf,
eqtt_to_assert,
bag_size_single_lemma,
false_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
bag_size_empty_lemma,
es-prior-interface_wf1,
es-E-interface_wf,
prior-val-val,
eclass-val_wf,
prior-val-as-latest-val,
es-latest-val_wf,
or-latest-val,
interface-or-val,
iff_weakening_equal,
is-latest-val,
es-le_weakening_eq,
es-le_wf,
eq_int_wf,
bag-size_wf,
nat_wf,
equal-wf-T-base,
bnot_wf,
not_wf,
squash_wf,
true_wf,
uiff_transitivity,
assert_of_eq_int,
iff_transitivity,
iff_weakening_uiff,
assert_of_bnot,
oobboth_wf,
bag-only_wf2,
single-valued-bag_wf,
less_than_wf,
bag_wf,
single-valued-bag-if-le1,
le_weakening,
decidable__lt,
le_antisymmetry_iff,
add_functionality_wrt_le,
add-zero,
le-add-cancel,
add-commutes,
zero-add,
oobleft_wf,
oobright_wf
Latex:
\mforall{}[Info,A,B:Type]. \mforall{}[X:EClass(A)]. \mforall{}[Y:EClass(B)].
((X |\msupminus{} Y))' = ((X)' | (Y)') supposing Singlevalued(X) \mwedge{} Singlevalued(Y)
Date html generated:
2015_07_21-PM-04_24_13
Last ObjectModification:
2015_02_04-PM-06_03_24
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