Nuprl Lemma : prior-val-as-latest-val
∀[Info,T:Type]. ∀[es:EO+(Info)]. ∀[X:EClass(T)]. ∀[e,p:E].
(((X)' es e) = ((X)- es p) ∈ bag(T)) supposing
((∀e'':E. ((e'' <loc e) ⇒ (p <loc e'') ⇒ (¬↑e'' ∈b X))) and
(p <loc e))
Proof
Definitions occuring in Statement :
es-latest-val: (X)-,
es-prior-val: (X)',
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-locl: (e <loc e'),
es-E: E,
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
apply: f a,
universe: Type,
equal: s = t ∈ T,
bag: bag(T)
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
member: t ∈ T,
all: ∀x:A. B[x],
implies: P ⇒ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
top: Top,
so_apply: x[s],
strongwellfounded: SWellFounded(R[x; y]),
exists: ∃x:A. B[x],
nat: ℕ,
false: False,
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
not: ¬A,
and: P ∧ Q,
guard: {T},
int_seg: {i..j-},
lelt: i ≤ j < k,
le: A ≤ B,
less_than': less_than'(a;b),
decidable: Dec(P),
or: P ∨ Q,
less_than: a < b,
squash: ↓T,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
bfalse: ff,
iff: P ⇐⇒ Q,
es-latest-val: (X)-,
rev_implies: P ⇐ Q,
true: True,
rev_uimplies: rev_uimplies(P;Q),
eclass: EClass(A[eo; e])
Latex:
\mforall{}[Info,T:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[X:EClass(T)]. \mforall{}[e,p:E].
(((X)' es e) = ((X)\msupminus{} es p)) supposing
((\mforall{}e'':E. ((e'' <loc e) {}\mRightarrow{} (p <loc e'') {}\mRightarrow{} (\mneg{}\muparrow{}e'' \mmember{}\msubb{} X))) and
(p <loc e))
Date html generated:
2016_05_17-AM-06_38_17
Last ObjectModification:
2016_01_17-PM-06_36_53
Theory : event-ordering
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