Nuprl Lemma : eo-strict-forward-pred?
∀[Info:Type]. ∀[eo:EO+(Info)]. ∀[e:E].
∀e1:E. (es-pred?(eo>e;e1) = if loc(e) = loc(e1) ∧b (es-eq(eo) pred(e1) e) then inr ⋅ else es-pred?(eo;e1) fi ∈ (E?))
Proof
Definitions occuring in Statement :
eo-strict-forward: eo>e,
event-ordering+: EO+(Info),
es-pred?: es-pred?(es;e),
es-pred: pred(e),
es-eq: es-eq(es),
es-loc: loc(e),
es-E: E,
eq_id: a = b,
band: p ∧b q,
ifthenelse: if b then t else f fi ,
it: ⋅,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
unit: Unit,
apply: f a,
inr: inr x ,
union: left + right,
universe: Type,
equal: s = t ∈ T
Lemmas :
eo-strict-forward-E-subtype,
es-pred?_property,
es-E_wf,
eo-strict-forward_wf,
event-ordering+_subtype,
event-ordering+_wf,
es-pred?_wf,
es-locl_wf,
es-pred_wf,
es-locl-first,
assert_elim,
btrue_neq_bfalse,
assert_wf,
es-first_wf2,
unit_wf2,
Id_wf,
es-loc_wf,
es-causl_wf,
all_wf,
isect_wf,
or_wf,
equal_wf,
not_wf,
eo-strict-forward-loc,
eo-strict-forward-less,
eo-strict-forward-E-member,
decidable__equal_Id,
member-eo-strict-forward-E,
es-locl_transitivity2,
es-le_weakening_eq,
es-causl_transitivity2,
es-causl_weakening,
es-causle_weakening,
uiff_transitivity,
equal-wf-T-base,
eqtt_to_assert,
assert-eq-id,
bnot_wf,
eqff_to_assert,
assert_of_bnot,
iff_transitivity,
iff_weakening_uiff,
es-causle_weakening_eq,
and_wf,
es-causle_wf,
es-causl_irreflexivity,
eq_id_wf,
bool_wf,
es-eq_wf,
deq_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
assert-es-eq-E,
es-pred_property,
es-locl_irreflexivity,
es-pred-locl,
equal-unit,
it_wf
\mforall{}[Info:Type]. \mforall{}[eo:EO+(Info)]. \mforall{}[e:E].
\mforall{}e1:E
(es-pred?(eo>e;e1)
= if loc(e) = loc(e1) \mwedge{}\msubb{} (es-eq(eo) pred(e1) e) then inr \mcdot{} else es-pred?(eo;e1) fi )
Date html generated:
2015_07_17-PM-00_08_57
Last ObjectModification:
2015_01_28-AM-00_15_37
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