Nuprl Lemma : num-antecedents-property
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[Sys:EClass(Top)]. ∀[f:sys-antecedent(es;Sys)]. ∀[e:E(Sys)].
{((f (f^#f(e) e)) = (f^#f(e) e) ∈ E(Sys)) ∧ (∀[i:ℕ#f(e)]. (¬((f (f^i e)) = (f^i e) ∈ E(Sys))))}
Proof
Definitions occuring in Statement :
num-antecedents: #f(e),
sys-antecedent: sys-antecedent(es;Sys),
es-E-interface: E(X),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
fun_exp: f^n,
int_seg: {i..j-},
uall: ∀[x:A]. B[x],
top: Top,
guard: {T},
not: ¬A,
and: P ∧ Q,
apply: f a,
natural_number: $n,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
strongwellfounded: SWellFounded(R[x; y]),
exists: ∃x:A. B[x],
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
not: ¬A,
top: Top,
and: P ∧ Q,
prop: ℙ,
guard: {T},
sys-antecedent: sys-antecedent(es;Sys),
es-E-interface: E(X),
int_seg: {i..j-},
lelt: i ≤ j < k,
le: A ≤ B,
less_than': less_than'(a;b),
decidable: Dec(P),
or: P ∨ Q,
less_than: a < b,
squash: ↓T,
num-antecedents: #f(e),
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
bfalse: ff,
sq_type: SQType(T),
bnot: ¬bb,
assert: ↑b,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
true: True,
so_lambda: λ2x.t[x],
so_apply: x[s],
es-causle: e c≤ e',
sq_stable: SqStable(P),
compose: f o g,
label: ...$L... t,
iff: P ⇐⇒ Q
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[Sys:EClass(Top)]. \mforall{}[f:sys-antecedent(es;Sys)]. \mforall{}[e:E(Sys)].
\{((f (f\^{}\#f(e) e)) = (f\^{}\#f(e) e)) \mwedge{} (\mforall{}[i:\mBbbN{}\#f(e)]. (\mneg{}((f (f\^{}i e)) = (f\^{}i e))))\}
Date html generated:
2016_05_16-PM-02_48_25
Last ObjectModification:
2016_01_17-PM-07_34_23
Theory : event-ordering
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