Nuprl Lemma : es-E-interface-conditional-subtype_rel
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[X,Y,Z:EClass(Top)]. (E([X?Y]) ⊆r E(Z)) supposing ((E(Y) ⊆r E(Z)) and (E(X) ⊆r E(Z)))
Proof
Definitions occuring in Statement :
es-E-interface: E(X),
cond-class: [X?Y],
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
top: Top,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
es-E-interface: E(X),
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
or: P ∨ Q,
prop: ℙ
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[X,Y,Z:EClass(Top)].
(E([X?Y]) \msubseteq{}r E(Z)) supposing ((E(Y) \msubseteq{}r E(Z)) and (E(X) \msubseteq{}r E(Z)))
Date html generated:
2016_05_16-PM-02_53_01
Last ObjectModification:
2015_12_29-AM-11_26_42
Theory : event-ordering
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