Nuprl Lemma : decidable__exists-single-valued-classrel
∀[Info,T:Type]. ∀X:EClass(T). ∀es:EO+(Info). (single-valued-classrel(es;X;T) ⇒ (∀e:E. Dec(∃v:T. v ∈ X(e))))
Proof
Definitions occuring in Statement :
single-valued-classrel: single-valued-classrel(es;X;T),
classrel: v ∈ X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
decidable: Dec(P),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
implies: P ⇒ Q,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
single-valued-classrel: single-valued-classrel(es;X;T),
member: t ∈ T,
eclass: EClass(A[eo; e]),
subtype_rel: A ⊆r B,
nat: ℕ,
classrel: v ∈ X(e),
decidable: Dec(P),
or: P ∨ Q,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
guard: {T},
not: ¬A,
false: False,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
single-valued-bag: single-valued-bag(b;T),
exists: ∃x:A. B[x],
uimplies: b supposing a,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
squash: ↓T
Latex:
\mforall{}[Info,T:Type].
\mforall{}X:EClass(T). \mforall{}es:EO+(Info). (single-valued-classrel(es;X;T) {}\mRightarrow{} (\mforall{}e:E. Dec(\mexists{}v:T. v \mmember{} X(e))))
Date html generated:
2016_05_16-PM-01_46_13
Last ObjectModification:
2016_01_17-PM-07_47_28
Theory : event-ordering
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