Nuprl Lemma : iseg-es-before-is-before
∀[es:EO]. ∀[e,x:E]. ∀[L:E List]. L = before(x) ∈ (E List) supposing L @ [x] ≤ before(e)
Proof
Definitions occuring in Statement :
es-before: before(e),
es-E: E,
event_ordering: EO,
iseg: l1 ≤ l2,
append: as @ bs,
cons: [a / b],
nil: [],
list: T List,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Lemmas :
length_wf_nat,
equal_wf,
nat_wf,
member_append,
member_singleton,
l_member_wf,
member-es-before,
es-before-partition,
es-before-no_repeats,
no_repeats_wf,
list-decomp-no_repeats,
es-before_wf,
es-open-interval_wf,
iseg_wf,
es-E_wf,
append_wf,
cons_wf,
nil_wf,
list_wf,
event_ordering_wf
\mforall{}[es:EO]. \mforall{}[e,x:E]. \mforall{}[L:E List]. L = before(x) supposing L @ [x] \mleq{} before(e)
Date html generated:
2015_07_17-AM-08_44_37
Last ObjectModification:
2015_01_27-PM-02_28_26
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