Nuprl Lemma : es-local-pred-cases-sq
∀[Info:Type]
∀es:EO+(Info). ∀e:E. ∀P:{e':E| (e' <loc e)} ─→ 𝔹.
(¬↑first(e))
∧ (((↑(P pred(e))) ∧ (do-apply(last(P);e) ~ pred(e)))
∨ ((¬↑(P pred(e))) ∧ (↑can-apply(last(P);pred(e))) ∧ (do-apply(last(P);e) ~ do-apply(last(P);pred(e)))))
supposing ↑can-apply(last(P);e)
Proof
Definitions occuring in Statement :
es-local-pred: last(P),
event-ordering+: EO+(Info),
es-locl: (e <loc e'),
es-first: first(e),
es-pred: pred(e),
es-E: E,
assert: ↑b,
bool: 𝔹,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
not: ¬A,
or: P ∨ Q,
and: P ∧ Q,
set: {x:A| B[x]} ,
apply: f a,
function: x:A ─→ B[x],
universe: Type,
sqequal: s ~ t,
do-apply: do-apply(f;x),
can-apply: can-apply(f;x)
Lemmas :
es-first_wf2,
bool_wf,
eqtt_to_assert,
false_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
not_wf,
true_wf,
assert_wf,
isl_wf,
sq_exists_wf,
es-locl_wf,
es-pred_wf,
all_wf,
es-local-pred_wf,
or_wf,
es-pred-locl,
es-locl_transitivity2,
es-le_weakening,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
assert_witness,
es-local-pred_wf2,
subtype_rel_dep_function,
subtype_rel_sets,
subtype_rel_self,
set_wf,
subtype_rel_sum,
top_wf,
btrue_wf,
bfalse_wf
Latex:
\mforall{}[Info:Type]
\mforall{}es:EO+(Info). \mforall{}e:E. \mforall{}P:\{e':E| (e' <loc e)\} {}\mrightarrow{} \mBbbB{}.
(\mneg{}\muparrow{}first(e))
\mwedge{} (((\muparrow{}(P pred(e))) \mwedge{} (do-apply(last(P);e) \msim{} pred(e)))
\mvee{} ((\mneg{}\muparrow{}(P pred(e)))
\mwedge{} (\muparrow{}can-apply(last(P);pred(e)))
\mwedge{} (do-apply(last(P);e) \msim{} do-apply(last(P);pred(e)))))
supposing \muparrow{}can-apply(last(P);e)
Date html generated:
2015_07_20-PM-04_06_20
Last ObjectModification:
2015_01_27-PM-09_57_32
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