Nuprl Lemma : sys-antecedent-closure
∀[Info:Type]
∀es:EO+(Info). ∀X:EClass(Top). ∀fs:sys-antecedent(es;X) List. ∀s:fset(E(X)). ∃c:fset(E(X)). (c = fs closure of s)
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-eq: es-eq(es),
fset-closure: (c = fs closure of s),
fset: fset(T),
list: T List,
uall: ∀[x:A]. B[x],
top: Top,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
universe: Type
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],
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
es-E-interface: E(X),
sys-antecedent: sys-antecedent(es;Sys),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
prop: ℙ,
implies: P ⇒ Q,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
nat: ℕ,
false: False,
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
not: ¬A,
top: Top,
or: P ∨ Q,
cons: [a / b],
colength: colength(L),
guard: {T},
decidable: Dec(P),
nil: [],
it: ⋅,
sq_type: SQType(T),
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
es-causle: e c≤ e',
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
true: True
Latex:
\mforall{}[Info:Type]
\mforall{}es:EO+(Info). \mforall{}X:EClass(Top). \mforall{}fs:sys-antecedent(es;X) List. \mforall{}s:fset(E(X)).
\mexists{}c:fset(E(X)). (c = fs closure of s)
Date html generated:
2016_05_16-PM-02_49_10
Last ObjectModification:
2016_01_17-PM-07_28_40
Theory : event-ordering
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