Nuprl Lemma : es-prior-interface-cases
∀[Info:Type]
∀X:EClass(Top). ∀es:EO+(Info). ∀e:E.
(¬↑first(e))
∧ (((↑pred(e) ∈b X) ∧ (prior(X)(e) = pred(e) ∈ E))
∨ ((¬↑pred(e) ∈b X) ∧ (↑pred(e) ∈b prior(X)) ∧ (prior(X)(e) = prior(X)(pred(e)) ∈ E)))
supposing ↑e ∈b prior(X)
Proof
Definitions occuring in Statement :
es-prior-interface: prior(X),
eclass-val: X(e),
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-first: first(e),
es-pred: pred(e),
es-E: E,
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
all: ∀x:A. B[x],
not: ¬A,
or: P ∨ Q,
and: P ∧ Q,
universe: Type,
equal: s = t ∈ T
Lemmas :
es-local-pred_wf,
eq_int_wf,
bag-size_wf,
top_wf,
nat_wf,
es-E_wf,
event-ordering+_subtype,
or_wf,
sq_exists_wf,
es-locl_wf,
assert_wf,
all_wf,
not_wf,
bag_size_single_lemma,
bag_only_single_lemma,
bag_size_empty_lemma,
equal_wf,
es-first_wf2,
bool_wf,
eqtt_to_assert,
true_wf,
isect_wf,
es-pred_wf,
isl_wf,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
false_wf,
assert_of_eq_int
Latex:
\mforall{}[Info:Type]
\mforall{}X:EClass(Top). \mforall{}es:EO+(Info). \mforall{}e:E.
(\mneg{}\muparrow{}first(e))
\mwedge{} (((\muparrow{}pred(e) \mmember{}\msubb{} X) \mwedge{} (prior(X)(e) = pred(e)))
\mvee{} ((\mneg{}\muparrow{}pred(e) \mmember{}\msubb{} X) \mwedge{} (\muparrow{}pred(e) \mmember{}\msubb{} prior(X)) \mwedge{} (prior(X)(e) = prior(X)(pred(e)))))
supposing \muparrow{}e \mmember{}\msubb{} prior(X)
Date html generated:
2015_07_21-PM-02_43_51
Last ObjectModification:
2015_01_27-PM-09_53_18
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