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)
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
strongwellfounded: SWellFounded(R[x; y]),
exists: ∃x:A. B[x],
guard: {T},
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
prop: ℙ,
decidable: Dec(P),
or: P ∨ Q,
le: A ≤ B,
less_than': less_than'(a;b),
nat: ℕ,
es-E-interface: E(X),
ge: i ≥ j ,
less_than: a < b,
squash: ↓T,
so_lambda: λ2x.t[x],
sys-antecedent: sys-antecedent(es;Sys),
so_apply: x[s],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
true: True,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
sq_stable: SqStable(P),
es-causle: e c≤ e',
label: ...$L... t,
sq_type: SQType(T),
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
cand: A c∧ B
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:
2016_05_17-AM-08_05_44
Last ObjectModification:
2016_01_17-PM-02_48_16
Theory : event-ordering
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