Nuprl Lemma : eclass3-total
∀[Info,B,C:Type]. ∀[X:EClass(B ⟶ C)]. ∀[Y:EClass(B)]. ∀[es:EO+(Info)].
(es-total-class(es;eclass3(X;Y))) supposing (es-total-class(es;X) and es-total-class(es;Y))
Proof
Definitions occuring in Statement :
eclass3: eclass3(X;Y),
es-total-class: es-total-class(es;X),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
es-total-class: es-total-class(es;X),
all: ∀x:A. B[x],
class-ap: X(e),
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
uiff: uiff(P;Q),
cand: A c∧ B,
subtype_rel: A ⊆r B,
le: A ≤ B,
not: ¬A,
false: False,
nat: ℕ,
prop: ℙ,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Latex:
\mforall{}[Info,B,C:Type]. \mforall{}[X:EClass(B {}\mrightarrow{} C)]. \mforall{}[Y:EClass(B)]. \mforall{}[es:EO+(Info)].
(es-total-class(es;eclass3(X;Y))) supposing (es-total-class(es;X) and es-total-class(es;Y))
Date html generated:
2016_05_16-PM-02_13_45
Last ObjectModification:
2015_12_29-AM-11_50_05
Theory : event-ordering
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