Nuprl Lemma : State-comb-classrel-class
∀[Info,B,A:Type]. ∀[f:A ⟶ B ⟶ B]. ∀[init:Id ⟶ bag(B)].
∀X:EClass(A). ∀es:EO+(Info). ∀e:E. ∀[v:B]. (v ∈ State-comb(init;f;X)(e) ⇐⇒ v ∈ State-class(init;f;X)(e))
Proof
Definitions occuring in Statement :
State-comb: State-comb(init;f;X),
State-class: State-class(init;f;X),
classrel: v ∈ X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
Id: Id,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
function: x:A ⟶ B[x],
universe: Type,
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},
iff: P ⇐⇒ Q,
classrel: v ∈ X(e),
bag-member: x ↓∈ bs,
squash: ↓T,
rev_implies: P ⇐ Q,
decidable: Dec(P),
or: P ∨ Q,
less_than: a < b,
le: A ≤ B,
less_than': less_than'(a;b),
uiff: uiff(P;Q),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
State-comb: State-comb(init;f;X),
simple-comb-2: F|X, Y|,
simple-comb: simple-comb(F;Xs),
select: L[n],
cons: [a / b],
subtract: n - m,
eclass: EClass(A[eo; e]),
sq_type: SQType(T),
ifthenelse: if b then t else f fi ,
btrue: tt,
bfalse: ff,
sq_stable: SqStable(P),
es-p-local-pred: es-p-local-pred(es;P),
es-locl: (e <loc e'),
gt: i > j,
iterated_classrel: iterated_classrel(es;S;A;f;init;X;e;v),
cand: A c∧ B,
bool: 𝔹,
unit: Unit,
it: ⋅,
bnot: ¬bb,
assert: ↑b,
so_lambda: λ2x.t[x],
so_apply: x[s],
true: True,
es-E: E,
es-base-E: es-base-E(es),
Id: Id,
rev_uimplies: rev_uimplies(P;Q)
Latex:
\mforall{}[Info,B,A:Type]. \mforall{}[f:A {}\mrightarrow{} B {}\mrightarrow{} B]. \mforall{}[init:Id {}\mrightarrow{} bag(B)].
\mforall{}X:EClass(A). \mforall{}es:EO+(Info). \mforall{}e:E.
\mforall{}[v:B]. (v \mmember{} State-comb(init;f;X)(e) \mLeftarrow{}{}\mRightarrow{} v \mmember{} State-class(init;f;X)(e))
Date html generated:
2016_05_17-AM-09_57_05
Last ObjectModification:
2016_01_17-PM-11_12_21
Theory : classrel!lemmas
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