Nuprl Lemma : es-prior-interface-cases-sq
∀[Info:Type]
∀X:EClass(Top). ∀es:EO+(Info). ∀e:E.
(¬↑first(e))
∧ (((↑pred(e) ∈b X) ∧ (prior(X)(e) ~ pred(e)))
∨ ((¬↑pred(e) ∈b X) ∧ (↑pred(e) ∈b prior(X)) ∧ (prior(X)(e) ~ prior(X)(pred(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,
sqequal: s ~ t
Lemmas :
assert_witness,
in-eclass_wf,
es-prior-interface_wf0,
es-interface-subtype_rel2,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
top_wf,
subtype_top,
is-prior-interface,
es-locl-first,
assert_elim,
btrue_neq_bfalse,
assert_wf,
es-first_wf2,
decidable__assert,
es-pred_wf,
eclass_wf,
not_wf,
bag_only_single_lemma,
assert-bnot,
bool_subtype_base,
subtype_base_sq,
bool_cases_sqequal,
equal_wf,
eqff_to_assert,
eqtt_to_assert,
bool_wf,
empty-bag_wf,
single-bag_wf,
or_wf,
es-local-pred_wf,
all_wf,
es-locl_wf,
sq_exists_wf,
iff_weakening_uiff,
iff_transitivity,
bag_size_single_lemma,
assert_of_eq_int,
bag-size_wf,
eq_int_wf,
assert_of_bnot,
bnot_wf,
equal-wf-T-base,
uiff_transitivity,
bag_size_empty_lemma
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) \msim{} pred(e)))
\mvee{} ((\mneg{}\muparrow{}pred(e) \mmember{}\msubb{} X) \mwedge{} (\muparrow{}pred(e) \mmember{}\msubb{} prior(X)) \mwedge{} (prior(X)(e) \msim{} prior(X)(pred(e)))))
supposing \muparrow{}e \mmember{}\msubb{} prior(X)
Date html generated:
2015_07_21-PM-02_44_03
Last ObjectModification:
2015_07_16-AM-09_42_22
Home
Index