Nuprl Lemma : es-pred-maximal-base
∀es:EO. ∀e:es-base-E(es). ∀e':E. ((loc(e') = loc(e) ∈ Id) ⇒ (e' < e) ⇒ (pred(e) < e') ⇒ False)
Proof
Definitions occuring in Statement :
es-pred: pred(e),
es-causl: (e < e'),
es-loc: loc(e),
es-E: E,
es-base-E: es-base-E(es),
event_ordering: EO,
Id: Id,
all: ∀x:A. B[x],
implies: P ⇒ Q,
false: False,
equal: s = t ∈ T
Lemmas :
event_ordering_wf,
es-loc-wf-base,
es-causl-wf-base,
es-eq-wf-base,
es-pred-wf-base,
es-causl-swellfnd-base,
nat_properties,
less_than_transitivity1,
less_than_irreflexivity,
ge_wf,
less_than_wf,
es-E_wf,
Id_wf,
es-base-E_wf,
int_seg_wf,
int_seg_subtype-nat,
decidable__le,
subtract_wf,
false_wf,
not-ge-2,
less-iff-le,
condition-implies-le,
minus-one-mul,
zero-add,
minus-add,
minus-minus,
add-associates,
add-swap,
add-commutes,
add_functionality_wrt_le,
add-zero,
le-add-cancel,
decidable__equal_int,
subtype_rel-int_seg,
le_weakening,
int_seg_properties,
le_wf,
nat_wf,
zero-le-nat,
lelt_wf,
equal_wf,
decidable__lt,
not-equal-2,
le-add-cancel-alt,
not-le-2,
sq_stable__le,
add-mul-special,
zero-mul,
es-dom_wf,
es-base-pred_wf,
bool_wf,
eqtt_to_assert,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
es-base-pred-properties,
es-eq-E-wf-base,
es-causl_transitivity,
es-causal-antireflexive,
es-causl-total-base,
assert_wf,
sq_stable__assert
\mforall{}es:EO. \mforall{}e:es-base-E(es). \mforall{}e':E. ((loc(e') = loc(e)) {}\mRightarrow{} (e' < e) {}\mRightarrow{} (pred(e) < e') {}\mRightarrow{} False)
Date html generated:
2015_07_17-AM-08_35_19
Last ObjectModification:
2015_01_27-PM-03_00_41
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