Nuprl Lemma : primed-class-opt-es-sv
∀[Info,B:Type]. ∀[es:EO+(Info)]. ∀[X:EClass(B)]. ∀[init:Id ⟶ bag(B)].
((∀l:Id. (#(init l) ≤ 1)) ⇒ es-sv-class(es;X) ⇒ es-sv-class(es;Prior(X)?init))
Proof
Definitions occuring in Statement :
primed-class-opt: Prior(X)?b,
es-sv-class: es-sv-class(es;X),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
Id: Id,
uall: ∀[x:A]. B[x],
le: A ≤ B,
all: ∀x:A. B[x],
implies: P ⇒ Q,
apply: f a,
function: x:A ⟶ B[x],
natural_number: $n,
universe: Type,
bag-size: #(bs),
bag: bag(T)
Definitions unfolded in proof :
primed-class-opt: Prior(X)?b,
es-sv-class: es-sv-class(es;X),
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
eclass: EClass(A[eo; e]),
subtype_rel: A ⊆r B,
implies: P ⇒ Q,
so_lambda: λ2x.t[x],
so_apply: x[s],
prop: ℙ,
uimplies: b supposing a,
do-apply: do-apply(f;x),
can-apply: can-apply(f;x),
and: P ∧ Q,
or: P ∨ Q,
isl: isl(x),
outl: outl(x),
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
sq_exists: ∃x:{A| B[x]},
not: ¬A,
false: False,
bfalse: ff,
nat: ℕ,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
le: A ≤ B
Latex:
\mforall{}[Info,B:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[X:EClass(B)]. \mforall{}[init:Id {}\mrightarrow{} bag(B)].
((\mforall{}l:Id. (\#(init l) \mleq{} 1)) {}\mRightarrow{} es-sv-class(es;X) {}\mRightarrow{} es-sv-class(es;Prior(X)?init))
Date html generated:
2016_05_17-AM-09_16_27
Last ObjectModification:
2015_12_29-PM-04_10_42
Theory : classrel!lemmas
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