Nuprl Lemma : cut-order_transitivity
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[X:EClass(Top)]. ∀[f:sys-antecedent(es;X)]. ∀[a,b,c:E(X)].
(a ≤(X;f) c) supposing (b ≤(X;f) c and a ≤(X;f) b)
Proof
Definitions occuring in Statement :
cut-order: a ≤(X;f) b,
sys-antecedent: sys-antecedent(es;Sys),
es-E-interface: E(X),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
universe: Type
Definitions unfolded in proof :
so_apply: x[s1;s2],
subtype_rel: A ⊆r B,
so_lambda: λ2x y.t[x; y],
prop: ℙ,
implies: P ⇒ Q,
cut-order: a ≤(X;f) b,
uimplies: b supposing a,
member: t ∈ T,
uall: ∀[x:A]. B[x],
and: P ∧ Q,
uiff: uiff(P;Q),
es-cut: Cut(X;f),
guard: {T},
f-subset: xs ⊆ ys,
all: ∀x:A. B[x]
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[X:EClass(Top)]. \mforall{}[f:sys-antecedent(es;X)]. \mforall{}[a,b,c:E(X)].
(a \mleq{}(X;f) c) supposing (b \mleq{}(X;f) c and a \mleq{}(X;f) b)
Date html generated:
2016_05_17-AM-07_43_58
Last ObjectModification:
2015_12_28-PM-11_34_24
Theory : event-ordering
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