Nuprl Lemma : es-fix-fun-exp
∀[Info:Type]. ∀es:EO+(Info). ∀X:EClass(Top). ∀f:sys-antecedent(es;X). ∀e:E(X). (↓∃n:ℕ. (f**(e) = (f^n e) ∈ E(X)))
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-fix: f**(e),
fun_exp: f^n,
nat: ℕ,
uall: ∀[x:A]. B[x],
top: Top,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
squash: ↓T,
apply: f a,
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},
squash: ↓T,
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,
sys-antecedent: sys-antecedent(es;Sys),
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],
es-causle: e c≤ e',
iff: P ⇐⇒ Q
Latex:
\mforall{}[Info:Type]
\mforall{}es:EO+(Info). \mforall{}X:EClass(Top). \mforall{}f:sys-antecedent(es;X). \mforall{}e:E(X). (\mdownarrow{}\mexists{}n:\mBbbN{}. (f**(e) = (f\^{}n e)))
Date html generated:
2016_05_16-PM-02_47_32
Last ObjectModification:
2016_01_17-PM-07_33_41
Theory : event-ordering
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