Nuprl Lemma : chain-pullback
∀[Info:Type]
∀es:EO+(Info). ∀Sys:EClass(Top). ∀f:sys-antecedent(es;Sys). ∀b,e:E(Sys).
(b is f*(e)
⇒ ∃e':E(Sys). ((loc(e') = loc(e) ∈ Id) ∧ e' is f*(e) ∧ b is f*(e') ∧ (¬(loc(f e') = loc(e') ∈ Id)))
supposing ¬(loc(b) = loc(e) ∈ Id))
Proof
Definitions occuring in Statement :
sys-antecedent: sys-antecedent(es;Sys),
es-E-interface: E(X),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-loc: loc(e),
Id: Id,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
and: P ∧ Q,
apply: f a,
universe: Type,
equal: s = t ∈ T,
fun-connected: y is f*(x)
Lemmas :
es-causl-swellfnd,
event-ordering+_subtype,
less_than_transitivity1,
less_than_irreflexivity,
int_seg_wf,
decidable__equal_int,
subtype_rel-int_seg,
false_wf,
le_weakening,
subtract_wf,
int_seg_properties,
le_wf,
nat_wf,
zero-le-nat,
lelt_wf,
es-causl_wf,
equal_wf,
all_wf,
int_seg_subtype-nat,
fun-connected_wf,
not_wf,
Id_wf,
es-loc_wf,
exists_wf,
decidable__lt,
not-equal-2,
condition-implies-le,
minus-add,
minus-minus,
minus-one-mul,
add-swap,
add-commutes,
add-associates,
add_functionality_wrt_le,
zero-add,
le-add-cancel-alt,
less-iff-le,
le-add-cancel,
set_wf,
less_than_wf,
primrec-wf2,
decidable__le,
not-le-2,
sq_stable__le,
add-zero,
add-mul-special,
zero-mul,
es-E-interface_wf,
sys-antecedent_wf,
eclass_wf,
top_wf,
es-E_wf,
event-ordering+_wf,
decidable__equal_Id,
fun-connected_weakening_eq,
and_wf,
fun-connected-step-back,
fun-connected-fixedpoint,
iff_weakening_equal,
true_wf,
squash_wf,
sq_stable__es-causle,
assert_wf,
bool_subtype_base,
bool_wf,
subtype_base_sq,
assert_elim,
in-eclass_wf,
fun-connected_transitivity,
decidable__equal_es-E-interface,
fun-connected-step
Latex:
\mforall{}[Info:Type]
\mforall{}es:EO+(Info). \mforall{}Sys:EClass(Top). \mforall{}f:sys-antecedent(es;Sys). \mforall{}b,e:E(Sys).
(b is f*(e)
{}\mRightarrow{} \mexists{}e':E(Sys). ((loc(e') = loc(e)) \mwedge{} e' is f*(e) \mwedge{} b is f*(e') \mwedge{} (\mneg{}(loc(f e') = loc(e'))))
supposing \mneg{}(loc(b) = loc(e)))
Date html generated:
2015_07_21-PM-04_17_41
Last ObjectModification:
2015_07_16-AM-09_40_06
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