Nuprl Lemma : sys-antecedent-fixedpoint
∀[Info:Type]
∀es:EO+(Info). ∀Sys:EClass(Top). ∀f:sys-antecedent(es;Sys). ∀e:E(Sys).
∃n:ℕ. (((f (f^n e)) = (f^n e) ∈ E(Sys)) ∧ ¬((f (f^n - 1 e)) = (f^n - 1 e) ∈ E(Sys)) supposing 0 < n)
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),
fun_exp: f^n,
nat: ℕ,
less_than: a < b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
not: ¬A,
and: P ∧ Q,
apply: f a,
subtract: n - m,
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],
guard: {T},
and: P ∧ Q,
sys-antecedent: sys-antecedent(es;Sys),
exists: ∃x:A. B[x],
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
es-E-interface: E(X),
so_apply: x[s],
prop: ℙ,
cand: A c∧ B,
uimplies: b supposing a,
not: ¬A,
implies: P ⇒ Q,
false: False,
nat: ℕ,
decidable: Dec(P),
or: P ∨ Q,
less_than: a < b,
squash: ↓T,
satisfiable_int_formula: satisfiable_int_formula(fmla),
top: Top,
ge: i ≥ j ,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
int_seg: {i..j-},
lelt: i ≤ j < k
Latex:
\mforall{}[Info:Type]
\mforall{}es:EO+(Info). \mforall{}Sys:EClass(Top). \mforall{}f:sys-antecedent(es;Sys). \mforall{}e:E(Sys).
\mexists{}n:\mBbbN{}. (((f (f\^{}n e)) = (f\^{}n e)) \mwedge{} \mneg{}((f (f\^{}n - 1 e)) = (f\^{}n - 1 e)) supposing 0 < n)
Date html generated:
2016_05_16-PM-02_48_54
Last ObjectModification:
2016_01_17-PM-07_28_09
Theory : event-ordering
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