Nuprl Lemma : State1-functional
∀[Info,A,B:Type]. ∀[init:Id ⟶ B]. ∀[tr:Id ⟶ A ⟶ B ⟶ B]. ∀[X:EClass(A)].
∀es:EO+(Info). (single-valued-classrel(es;X;A) ⇒ State1(init;tr;X) is functional)
Proof
Definitions occuring in Statement :
State1: State1(init;tr;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,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
implies: P ⇒ Q,
State1: State1(init;tr;X),
uimplies: b supposing a,
top: Top,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
prop: ℙ,
es-functional-class: X is functional,
single-valued-classrel: single-valued-classrel(es;X;T),
subtype_rel: A ⊆r B,
es-total-class: es-total-class(es;X),
nat: ℕ,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Latex:
\mforall{}[Info,A,B:Type]. \mforall{}[init:Id {}\mrightarrow{} B]. \mforall{}[tr:Id {}\mrightarrow{} A {}\mrightarrow{} B {}\mrightarrow{} B]. \mforall{}[X:EClass(A)].
\mforall{}es:EO+(Info). (single-valued-classrel(es;X;A) {}\mRightarrow{} State1(init;tr;X) is functional)
Date html generated:
2016_05_17-AM-10_04_10
Last ObjectModification:
2015_12_29-PM-03_53_10
Theory : classrel!lemmas
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