Nuprl Lemma : State-loc-comb-is-loop-class-state
∀[Info,A,B:Type]. ∀[init:Id ⟶ bag(B)]. ∀[f:Id ⟶ A ⟶ B ⟶ B]. ∀[X:EClass(A)].
(State-loc-comb(init;f;X) = loop-class-state((f o X);init) ∈ EClass(B))
Proof
Definitions occuring in Statement :
State-loc-comb: State-loc-comb(init;f;X),
loop-class-state: loop-class-state(X;init),
eclass1: (f o X),
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,
State-loc-comb: State-loc-comb(init;f;X),
rec-combined-loc-class-opt-1: F|Loc, X, Prior(self)?init|,
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,
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,
select: L[n],
cons: [a / b],
rec-comb: rec-comb(X;f;init),
loop-class-state: loop-class-state(X;init),
class-ap: X(e),
eclass-cond: eclass-cond(X;Y),
eclass3: eclass3(X;Y),
member-eclass: e ∈b X,
eclass1: (f o X),
sq_type: SQType(T),
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
eclass: EClass(A[eo; e]),
ifthenelse: if b then t else f fi ,
bnot: ¬bb,
bfalse: ff,
assert: ↑b,
lifting-loc-2: lifting-loc-2(f),
lifting2-loc: lifting2-loc(f;loc;abag;bbag),
lifting-loc-gen-rev: lifting-loc-gen-rev(n;bags;loc;f),
lifting-gen-rev: lifting-gen-rev(n;f;bags),
lifting-gen-list-rev: lifting-gen-list-rev(n;bags),
eq_int: (i =z j),
subtract: n - m,
so_lambda: λ2x.t[x],
so_apply: x[s],
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
true: True
Latex:
\mforall{}[Info,A,B:Type]. \mforall{}[init:Id {}\mrightarrow{} bag(B)]. \mforall{}[f:Id {}\mrightarrow{} A {}\mrightarrow{} B {}\mrightarrow{} B]. \mforall{}[X:EClass(A)].
(State-loc-comb(init;f;X) = loop-class-state((f o X);init))
Date html generated:
2016_05_17-AM-10_00_47
Last ObjectModification:
2016_01_17-PM-11_06_18
Theory : classrel!lemmas
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