Nuprl Lemma : eclass-ext-classrel
∀[Info,T:Type]. ∀[X,Y:EClass(T)].
uiff(X = Y ∈ EClass(T);∀es:EO+(Info). ∀e:E. ∀v:T. (v ∈ X(e) ⇐⇒ v ∈ Y(e)))
supposing ∀es:EO+(Info). ∀e:E. ((#(X es e) ≤ 1) ∧ (#(Y es e) ≤ 1))
Proof
Definitions occuring in Statement :
classrel: v ∈ X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
uiff: uiff(P;Q),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
le: A ≤ B,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
apply: f a,
natural_number: $n,
universe: Type,
equal: s = t ∈ T,
bag-size: #(bs)
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
uiff: uiff(P;Q),
and: P ∧ Q,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
so_lambda: λ2x y.t[x; y],
subtype_rel: A ⊆r B,
so_apply: x[s1;s2],
prop: ℙ,
rev_implies: P ⇐ Q,
classrel: v ∈ X(e),
bag-member: x ↓∈ bs,
squash: ↓T,
eclass: EClass(A[eo; e]),
cand: A c∧ B,
not: ¬A,
false: False,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top,
so_lambda: λ2x.t[x],
so_apply: x[s],
guard: {T},
rev_uimplies: rev_uimplies(P;Q)
Latex:
\mforall{}[Info,T:Type]. \mforall{}[X,Y:EClass(T)].
uiff(X = Y;\mforall{}es:EO+(Info). \mforall{}e:E. \mforall{}v:T. (v \mmember{} X(e) \mLeftarrow{}{}\mRightarrow{} v \mmember{} Y(e)))
supposing \mforall{}es:EO+(Info). \mforall{}e:E. ((\#(X es e) \mleq{} 1) \mwedge{} (\#(Y es e) \mleq{} 1))
Date html generated:
2016_05_16-PM-01_35_44
Last ObjectModification:
2016_01_17-PM-07_54_55
Theory : event-ordering
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