Nuprl Lemma : es-E-interface-image
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[A,B:Type]. ∀[f:A ⟶ B]. ∀[Ia:EClass(A)]. ((E(f'Ia) ⊆r E(Ia)) ∧ (E(Ia) ⊆r E(f'Ia)))
Proof
Definitions occuring in Statement :
es-E-interface: E(X),
es-interface-image: f'Ia,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
and: P ∧ Q,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
and: P ∧ Q,
cand: A c∧ B,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
all: ∀x:A. B[x],
top: Top,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
implies: P ⇒ Q,
prop: ℙ
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[A,B:Type]. \mforall{}[f:A {}\mrightarrow{} B]. \mforall{}[Ia:EClass(A)].
((E(f'Ia) \msubseteq{}r E(Ia)) \mwedge{} (E(Ia) \msubseteq{}r E(f'Ia)))
Date html generated:
2016_05_16-PM-10_21_19
Last ObjectModification:
2015_12_29-AM-11_12_30
Theory : event-ordering
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