Nuprl Lemma : State-comb-exists-iff
∀[Info,B,A:Type]. ∀[f:A ⟶ B ⟶ B]. ∀[init:Id ⟶ bag(B)].
∀X:EClass(A). ∀[es:EO+(Info)]. ∀[e:E]. uiff(#(init loc(e)) > 0;↓∃v:B. v ∈ State-comb(init;f;X)(e))
Proof
Definitions occuring in Statement :
State-comb: State-comb(init;f;X),
classrel: v ∈ X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-loc: loc(e),
es-E: E,
Id: Id,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
gt: i > j,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
squash: ↓T,
apply: f a,
function: x:A ⟶ B[x],
natural_number: $n,
universe: Type,
bag-size: #(bs),
bag: bag(T)
Definitions unfolded in proof :
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
member: t ∈ T,
uall: ∀[x:A]. B[x],
squash: ↓T,
prop: ℙ,
subtype_rel: A ⊆r B,
nat: ℕ,
gt: i > j,
all: ∀x:A. B[x],
strongwellfounded: SWellFounded(R[x; y]),
exists: ∃x:A. B[x],
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
not: ¬A,
top: Top,
guard: {T},
so_lambda: λ2x.t[x],
so_apply: x[s],
decidable: Dec(P),
or: P ∨ Q,
less_than: a < b,
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,
classrel: v ∈ X(e),
eclass: EClass(A[eo; e]),
sq_type: SQType(T),
ifthenelse: if b then t else f fi ,
btrue: tt,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
bfalse: ff,
le: A ≤ B,
less_than': less_than'(a;b),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
es-p-local-pred: es-p-local-pred(es;P),
es-locl: (e <loc e')
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]. uiff(\#(init loc(e)) > 0;\mdownarrow{}\mexists{}v:B. v \mmember{} State-comb(init;f;X)(e))
Date html generated:
2016_05_17-AM-09_56_23
Last ObjectModification:
2016_01_17-PM-11_07_19
Theory : classrel!lemmas
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