Nuprl Lemma : loop-class-memory-is-prior-loop-class-state
∀[Info,B:Type]. ∀[X:EClass(B ⟶ B)]. ∀[init:Id ⟶ bag(B)].
(loop-class-memory(X;init) = Prior(loop-class-state(X;init))?init ∈ EClass(B))
Proof
Definitions occuring in Statement :
loop-class-memory: loop-class-memory(X;init),
loop-class-state: loop-class-state(X;init),
primed-class-opt: Prior(X)?b,
eclass: EClass(A[eo; e]),
Id: Id,
uall: ∀[x:A]. B[x],
function: x:A ⟶ B[x],
universe: Type,
equal: s = t ∈ T,
bag: bag(T)
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
and: P ∧ Q,
cand: A c∧ B,
exists: ∃x:A. B[x],
so_lambda: λ2x y.t[x; y],
subtype_rel: A ⊆r B,
so_apply: x[s1;s2],
uimplies: b supposing a,
all: ∀x:A. B[x],
strongwellfounded: SWellFounded(R[x; y]),
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
not: ¬A,
top: Top,
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,
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,
sq_type: SQType(T),
bnot: ¬bb,
assert: ↑b,
loop-class-state: loop-class-state(X;init),
eclass-cond: eclass-cond(X;Y),
eclass3: eclass3(X;Y),
class-ap: X(e),
member-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
lt_int: i <z j
Latex:
\mforall{}[Info,B:Type]. \mforall{}[X:EClass(B {}\mrightarrow{} B)]. \mforall{}[init:Id {}\mrightarrow{} bag(B)].
(loop-class-memory(X;init) = Prior(loop-class-state(X;init))?init)
Date html generated:
2016_05_16-PM-11_41_29
Last ObjectModification:
2016_01_17-PM-07_07_47
Theory : event-ordering
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