Nuprl Lemma : State-comb-functional
∀[Info,B,A:Type]. ∀[f:A ⟶ B ⟶ B]. ∀[init:Id ⟶ bag(B)]. ∀[X:EClass(A)]. ∀[es:EO+(Info)].
(State-comb(init;f;X) is functional) supposing
(single-valued-classrel(es;X;A) and
(∀l:Id. single-valued-bag(init l;B)) and
(∀l:Id. (1 ≤ #(init l))))
Proof
Definitions occuring in Statement :
State-comb: State-comb(init;f;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,
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),
all: ∀x:A. B[x],
implies: P ⇒ Q,
es-total-class: es-total-class(es;X),
le: A ≤ B,
not: ¬A,
false: False
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)].
(State-comb(init;f;X) is functional) supposing
(single-valued-classrel(es;X;A) and
(\mforall{}l:Id. single-valued-bag(init l;B)) and
(\mforall{}l:Id. (1 \mleq{} \#(init l))))
Date html generated:
2016_05_17-AM-09_58_10
Last ObjectModification:
2015_12_29-PM-03_56_50
Theory : classrel!lemmas
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