Nuprl Lemma : es-prior-val-equal
∀[Info,T:Type]. ∀[X,Y:EClass(T)]. ∀[es:EO+(Info)]. ∀[e:E].
((X)' es e) = ((Y)' es e) ∈ bag(T) supposing ∀e':E. ((e' <loc e) ⇒ ((X es e') = (Y es e') ∈ bag(T)))
Proof
Definitions occuring in Statement :
es-prior-val: (X)',
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-locl: (e <loc e'),
es-E: E,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
apply: f a,
universe: Type,
equal: s = t ∈ T,
bag: bag(T)
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
prop: ℙ,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
eclass: EClass(A[eo; e]),
so_apply: x[s],
in-eclass: e ∈b X,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
nat: ℕ,
rev_implies: P ⇐ Q,
squash: ↓T,
true: True,
guard: {T},
uiff: uiff(P;Q),
es-prior-val: (X)',
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
top: Top,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
bfalse: ff,
es-locl: (e <loc e'),
or: P ∨ Q,
rev_uimplies: rev_uimplies(P;Q),
es-E-interface: E(X),
not: ¬A,
false: False,
sq_type: SQType(T),
assert: ↑b,
eclass-val: X(e),
cand: A c∧ B,
decidable: Dec(P),
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x]
Latex:
\mforall{}[Info,T:Type]. \mforall{}[X,Y:EClass(T)]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E].
((X)' es e) = ((Y)' es e) supposing \mforall{}e':E. ((e' <loc e) {}\mRightarrow{} ((X es e') = (Y es e')))
Date html generated:
2016_05_17-AM-06_30_22
Last ObjectModification:
2016_01_17-PM-06_41_20
Theory : event-ordering
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