Nuprl Lemma : es-pred-less-base
∀es:EO. ∀e:es-base-E(es). ((¬(pred(e) = e ∈ es-base-E(es))) ⇒ (pred(e) < e))
Proof
Definitions occuring in Statement :
es-pred: pred(e),
es-causl: (e < e'),
es-base-E: es-base-E(es),
event_ordering: EO,
all: ∀x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
equal: s = t ∈ T
Lemmas :
es-pred-wf-base,
event_ordering_wf,
es-causl-wf-base,
es-eq-wf-base,
es-causl-swellfnd-base,
nat_properties,
less_than_transitivity1,
less_than_irreflexivity,
ge_wf,
less_than_wf,
not_wf,
equal_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,
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-less,
assert-es-eq-E-base,
es-eq-E-wf-base,
assert_wf,
deq_wf,
decidable__equal-es-base-E,
es-causl_transitivity
\mforall{}es:EO. \mforall{}e:es-base-E(es). ((\mneg{}(pred(e) = e)) {}\mRightarrow{} (pred(e) < e))
Date html generated:
2015_07_17-AM-08_35_12
Last ObjectModification:
2015_01_27-PM-03_00_49
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