Nuprl Lemma : es-first-at-implies-first-at
∀es:EO. ∀i:Id.
∀[P:{e:E| loc(e) = i ∈ Id} ─→ ℙ]
∀e:E
(e is first@ i s.t. e.P[e]
⇒ {∀[Q:{e:E| loc(e) = i ∈ Id} ─→ ℙ]
(e is first@ i s.t. e.Q[e] ⇐⇒ Q[e] ∧ ∀e'<e.e' is first@ i s.t. e.Q[e] ⇒ P[e'])})
Proof
Definitions occuring in Statement :
es-first-at: e is first@ i s.t. e.P[e],
alle-lt: ∀e<e'.P[e],
es-loc: loc(e),
es-E: E,
event_ordering: EO,
Id: Id,
uall: ∀[x:A]. B[x],
prop: ℙ,
guard: {T},
so_apply: x[s],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
and: P ∧ Q,
set: {x:A| B[x]} ,
function: x:A ─→ B[x],
equal: s = t ∈ T
Lemmas :
es-loc_wf,
es-first-at_wf,
es-locl_wf,
Id_wf,
es-E_wf,
es-causl-swellfnd,
nat_properties,
less_than_transitivity1,
less_than_irreflexivity,
ge_wf,
less_than_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,
es-causl_wf,
es-causl_weakening,
es-locl_transitivity2,
es-le_weakening,
equal_wf,
decidable__lt,
not-equal-2,
le-add-cancel-alt,
not-le-2,
sq_stable__le,
add-mul-special,
zero-mul,
alle-lt_wf,
event_ordering_wf
\mforall{}es:EO. \mforall{}i:Id.
\mforall{}[P:\{e:E| loc(e) = i\} {}\mrightarrow{} \mBbbP{}]
\mforall{}e:E
(e is first@ i s.t. e.P[e]
{}\mRightarrow{} \{\mforall{}[Q:\{e:E| loc(e) = i\} {}\mrightarrow{} \mBbbP{}]
(e is first@ i s.t. e.Q[e] \mLeftarrow{}{}\mRightarrow{} Q[e] \mwedge{} \mforall{}e'<e.e' is first@ i s.t. e.Q[e] {}\mRightarrow{} P[e'])\})
Date html generated:
2015_07_17-AM-08_50_21
Last ObjectModification:
2015_01_27-PM-01_20_30
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