Nuprl Lemma : pair-prior-val
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[A,B:Type]. ∀[X:EClass(A)]. ∀[Y:EClass(B)]. ∀[e:E]. X;Y(e) ~ <(X)'(e), Y(e)> supposing \000C↑e ∈b X;Y
Proof
Definitions occuring in Statement :
es-interface-pair-prior: X;Y,
es-prior-val: (X)',
eclass-val: X(e),
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
pair: <a, b>,
universe: Type,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
all: ∀x:A. B[x],
top: Top,
uiff: uiff(P;Q),
and: P ∧ Q,
es-interface-pair-prior: X;Y,
eclass-val: X(e),
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
band: p ∧b q,
ifthenelse: if b then t else f fi ,
bfalse: ff,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
not: ¬A
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[A,B:Type]. \mforall{}[X:EClass(A)]. \mforall{}[Y:EClass(B)]. \mforall{}[e:E].
X;Y(e) \msim{} <(X)'(e), Y(e)> supposing \muparrow{}e \mmember{}\msubb{} X;Y
Date html generated:
2016_05_17-AM-07_17_16
Last ObjectModification:
2015_12_29-AM-00_01_10
Theory : event-ordering
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