Nuprl Lemma : Memory-loc-class-functional
∀[Info,A,S:Type]. ∀[init:Id ⟶ bag(S)]. ∀[f:Id ⟶ A ⟶ S ⟶ S]. ∀[X:EClass(A)]. ∀[es:EO+(Info)].
(Memory-loc-class(f;init;X) is functional) supposing
(single-valued-classrel(es;X;A) and
(∀l:Id. single-valued-bag(init l;S)) and
(∀l:Id. (1 ≤ #(init l))))
Proof
Definitions occuring in Statement :
Memory-loc-class: Memory-loc-class(f;init;X),
es-functional-class: X is functional,
single-valued-classrel: single-valued-classrel(es;X;T),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
Id: Id,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
le: A ≤ B,
all: ∀x:A. B[x],
apply: f a,
function: x:A ⟶ B[x],
natural_number: $n,
universe: Type,
single-valued-bag: single-valued-bag(b;T),
bag-size: #(bs),
bag: bag(T)
Definitions unfolded in proof :
es-functional-class: X is functional,
and: P ∧ Q,
cand: A c∧ B,
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
implies: P ⇒ Q,
uimplies: b supposing a,
prop: ℙ,
subtype_rel: A ⊆r B,
nat: ℕ,
so_lambda: λ2x.t[x],
so_apply: x[s],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
single-valued-classrel: single-valued-classrel(es;X;T),
es-total-class: es-total-class(es;X),
le: A ≤ B,
not: ¬A,
false: False
Latex:
\mforall{}[Info,A,S:Type]. \mforall{}[init:Id {}\mrightarrow{} bag(S)]. \mforall{}[f:Id {}\mrightarrow{} A {}\mrightarrow{} S {}\mrightarrow{} S]. \mforall{}[X:EClass(A)]. \mforall{}[es:EO+(Info)].
(Memory-loc-class(f;init;X) is functional) supposing
(single-valued-classrel(es;X;A) and
(\mforall{}l:Id. single-valued-bag(init l;S)) and
(\mforall{}l:Id. (1 \mleq{} \#(init l))))
Date html generated:
2016_05_17-AM-09_23_56
Last ObjectModification:
2015_12_29-PM-04_05_20
Theory : classrel!lemmas
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