Nuprl Lemma : loop-class-memory-no-input
∀[Info,B:Type]. ∀[X:EClass(B ⟶ B)]. ∀[init:Id ⟶ bag(B)]. ∀[es:EO+(Info)]. ∀[e:E].
loop-class-memory(X;init)(e) = Prior(loop-class-memory(X;init))?init(e) ∈ bag(B)
supposing (¬↑first(e)) ⇒ (¬↑pred(e) ∈b X)
Proof
Definitions occuring in Statement :
loop-class-memory: loop-class-memory(X;init),
primed-class-opt: Prior(X)?b,
member-eclass: e ∈b X,
class-ap: X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-first: first(e),
es-pred: pred(e),
es-E: E,
Id: Id,
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
not: ¬A,
implies: P ⇒ Q,
function: x:A ⟶ B[x],
universe: Type,
equal: s = t ∈ T,
bag: bag(T)
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
strongwellfounded: SWellFounded(R[x; y]),
exists: ∃x:A. B[x],
uall: ∀[x:A]. B[x],
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
not: ¬A,
top: Top,
and: P ∧ Q,
prop: ℙ,
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,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
class-ap: X(e),
loop-class-memory: loop-class-memory(X;init),
so_lambda: λ2x.t[x],
so_apply: x[s],
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
bfalse: ff,
es-E: E,
es-base-E: es-base-E(es),
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
classrel: v ∈ X(e),
rev_uimplies: rev_uimplies(P;Q),
bag-null: bag-null(bs)
Latex:
\mforall{}[Info,B:Type]. \mforall{}[X:EClass(B {}\mrightarrow{} B)]. \mforall{}[init:Id {}\mrightarrow{} bag(B)]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E].
loop-class-memory(X;init)(e) = Prior(loop-class-memory(X;init))?init(e)
supposing (\mneg{}\muparrow{}first(e)) {}\mRightarrow{} (\mneg{}\muparrow{}pred(e) \mmember{}\msubb{} X)
Date html generated:
2016_05_16-PM-11_40_07
Last ObjectModification:
2016_01_17-PM-07_14_38
Theory : event-ordering
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