Nuprl Lemma : rec-combined-class-opt-1-single-val0
∀[Info,A,B:Type]. ∀[es:EO+(Info)]. ∀[F:A ⟶ B ⟶ B]. ∀[X:EClass(A)]. ∀[init:Id ⟶ bag(B)]. ∀[e:E]. ∀[v1,v2:B].
(v1 = v2 ∈ B) supposing
(v1 ∈ lifting-2(F)|X,Prior(self)?init|(e) and
v2 ∈ lifting-2(F)|X,Prior(self)?init|(e) and
single-valued-classrel(es;X;A) and
single-valued-bag(init loc(e);B))
Proof
Definitions occuring in Statement :
rec-combined-class-opt-1: F|X,Prior(self)?init|,
single-valued-classrel: single-valued-classrel(es;X;T),
classrel: v ∈ X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-loc: loc(e),
es-E: E,
Id: Id,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
apply: f a,
function: x:A ⟶ B[x],
universe: Type,
equal: s = t ∈ T,
lifting-2: lifting-2(f),
single-valued-bag: single-valued-bag(b;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},
decidable: Dec(P),
or: P ∨ Q,
less_than: a < b,
squash: ↓T,
uiff: uiff(P;Q),
single-valued-classrel: single-valued-classrel(es;X;T),
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),
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
es-locl: (e <loc e'),
single-valued-bag: single-valued-bag(b;T)
Latex:
\mforall{}[Info,A,B:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[F:A {}\mrightarrow{} B {}\mrightarrow{} B]. \mforall{}[X:EClass(A)]. \mforall{}[init:Id {}\mrightarrow{} bag(B)]. \mforall{}[e:E].
\mforall{}[v1,v2:B].
(v1 = v2) supposing
(v1 \mmember{} lifting-2(F)|X,Prior(self)?init|(e) and
v2 \mmember{} lifting-2(F)|X,Prior(self)?init|(e) and
single-valued-classrel(es;X;A) and
single-valued-bag(init loc(e);B))
Date html generated:
2016_05_17-AM-09_30_04
Last ObjectModification:
2016_01_17-PM-11_09_43
Theory : classrel!lemmas
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