Nuprl Lemma : eo-forward-pred?
∀[Info:Type]. ∀[eo:EO+(Info)]. ∀[e:E].
∀e1:E. (es-pred?(eo.e;e1) = if es-eq(eo) e1 e then inr ⋅ else es-pred?(eo;e1) fi ∈ (E?))
Proof
Definitions occuring in Statement :
eo-forward: eo.e,
event-ordering+: EO+(Info),
es-pred?: es-pred?(es;e),
es-eq: es-eq(es),
es-E: E,
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-forward-E-subtype,
es-first_wf2,
bool_wf,
eqtt_to_assert,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
es-E_wf,
eo-forward_wf,
event-ordering+_subtype,
event-ordering+_wf,
es-eq-E_wf,
assert-es-eq-E-2,
it_wf,
eo-forward-first,
eq_id_wf,
es-loc_wf,
assert_wf,
bnot_wf,
not_wf,
Id_wf,
bool_cases,
assert-eq-id,
iff_transitivity,
iff_weakening_uiff,
assert_of_bnot,
assert-es-eq-E,
unit_wf2,
eo-forward-pred,
es-pred_wf,
iff_weakening_equal,
eo-forward-loc,
and_wf,
eo-forward-E-member,
es-locl-first,
assert_elim,
btrue_neq_bfalse
\mforall{}[Info:Type]. \mforall{}[eo:EO+(Info)]. \mforall{}[e:E].
\mforall{}e1:E. (es-pred?(eo.e;e1) = if es-eq(eo) e1 e then inr \mcdot{} else es-pred?(eo;e1) fi )
Date html generated:
2015_07_17-PM-00_04_13
Last ObjectModification:
2015_02_04-PM-05_40_47
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