Nuprl Lemma : assert-es-first
∀[es:EO]. ∀[e:E]. uiff(↑first(e);∀[e':E]. ¬(e' < e) supposing loc(e') = loc(e) ∈ Id)
Proof
Definitions occuring in Statement :
es-first: first(e),
es-causl: (e < e'),
es-loc: loc(e),
es-E: E,
event_ordering: EO,
Id: Id,
assert: ↑b,
uiff: uiff(P;Q),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
not: ¬A,
equal: s = t ∈ T
Lemmas :
es-causl_wf,
equal_wf,
Id_wf,
es-loc_wf,
es-E_wf,
assert_wf,
es-first_wf,
assert_witness,
uall_wf,
isect_wf,
not_wf,
event_ordering_wf,
es-eq-E-wf-base,
es-loc-wf-base,
es-causl-wf-base,
es-pred-wf-base,
es-causl-swellfnd-base,
nat_properties,
less_than_transitivity1,
less_than_irreflexivity,
ge_wf,
less_than_wf,
bor_wf,
bnot_wf,
es-dom_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-base-pred_wf,
bool_wf,
eqtt_to_assert,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
or_wf,
all_wf,
iff_transitivity,
iff_weakening_uiff,
assert_of_bor,
assert_of_bnot,
assert-es-eq-E-base,
es-base-pred-properties,
es-causal-antireflexive,
decidable__assert,
es-causl-total-base,
es-base-pred-le,
es-pred-cle,
es-causl_transitivity,
sq_stable__assert,
not_assert_elim,
and_wf,
assert_elim,
btrue_neq_bfalse,
es-pred_property,
es-pred_wf
\mforall{}[es:EO]. \mforall{}[e:E]. uiff(\muparrow{}first(e);\mforall{}[e':E]. \mneg{}(e' < e) supposing loc(e') = loc(e))
Date html generated:
2015_07_17-AM-08_35_50
Last ObjectModification:
2015_01_27-PM-03_01_01
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