Nuprl Lemma : primed-class-opt-es-sv0
∀[Info,B:Type]. ∀[es:EO+(Info)]. ∀[X:EClass(B)]. ∀[init:Id ⟶ bag(B)]. ∀[e:E].
((#(init loc(e)) ≤ 1) ⇒ (∀e':E. ((e' <loc e) ⇒ (#(X es e') ≤ 1))) ⇒ (#(Prior(X)?init es e) ≤ 1))
Proof
Definitions occuring in Statement :
primed-class-opt: Prior(X)?b,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-locl: (e <loc e'),
es-loc: loc(e),
es-E: E,
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,
member: t ∈ T,
uall: ∀[x:A]. B[x],
eclass: EClass(A[eo; e]),
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
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,
true: True,
sq_exists: ∃x:{A| B[x]},
sq_stable: SqStable(P),
squash: ↓T,
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{}[e:E].
((\#(init loc(e)) \mleq{} 1)
{}\mRightarrow{} (\mforall{}e':E. ((e' <loc e) {}\mRightarrow{} (\#(X es e') \mleq{} 1)))
{}\mRightarrow{} (\#(Prior(X)?init es e) \mleq{} 1))
Date html generated:
2016_05_17-AM-09_16_24
Last ObjectModification:
2016_01_17-PM-11_14_42
Theory : classrel!lemmas
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