Nuprl Lemma : latest-val-cases
∀[Info:Type]
∀es:EO+(Info)
∀[T:Type]
∀X:EClass(T). ∀e:E.
(↑e ∈b (X)- ⇐⇒ ((↑e ∈b X) ∧ ((X)-(e) = X(e) ∈ T)) ∨ (((↑e ∈b (X)') ∧ (¬↑e ∈b X)) ∧ ((X)-(e) = (X)'(e) ∈ T)))
Proof
Definitions occuring in Statement :
es-latest-val: (X)-,
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,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
not: ¬A,
or: P ∨ Q,
and: P ∧ Q,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
es-latest-val: (X)-,
in-eclass: e ∈b X,
eclass-val: X(e),
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
ifthenelse: if b then t else f fi ,
assert: ↑b,
top: Top,
eq_int: (i =z j),
bfalse: ff,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
false: False,
eclass: EClass(A[eo; e]),
nat: ℕ,
decidable: Dec(P),
satisfiable_int_formula: satisfiable_int_formula(fmla),
not: ¬A,
iff: P ⇐⇒ Q,
cand: A c∧ B,
true: True,
rev_implies: P ⇐ Q
Latex:
\mforall{}[Info:Type]
\mforall{}es:EO+(Info)
\mforall{}[T:Type]
\mforall{}X:EClass(T). \mforall{}e:E.
(\muparrow{}e \mmember{}\msubb{} (X)\msupminus{}
\mLeftarrow{}{}\mRightarrow{} ((\muparrow{}e \mmember{}\msubb{} X) \mwedge{} ((X)\msupminus{}(e) = X(e))) \mvee{} (((\muparrow{}e \mmember{}\msubb{} (X)') \mwedge{} (\mneg{}\muparrow{}e \mmember{}\msubb{} X)) \mwedge{} ((X)\msupminus{}(e) = (X)'(e))))
Date html generated:
2016_05_17-AM-06_36_36
Last ObjectModification:
2016_01_17-PM-06_36_10
Theory : event-ordering
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