Nuprl Lemma : Q-R-glues-empty
∀[Info:Type]
∀es:EO+(Info)
∀[Qa,Rb:E ⟶ E ⟶ ℙ]. ∀[A,B:Type].
∀Ia:EClass(A). ∀Ib:EClass(B). ∀f,g:Top.
(g glues Ia:Qa ──f⟶ Ib:Rb) supposing (es-interface-empty(es;Ib) and es-interface-empty(es;Ia))
Proof
Definitions occuring in Statement :
Q-R-glues: g glues Ia:Qa ──f⟶ Ib:Rb,
es-interface-empty: es-interface-empty(es;I),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
prop: ℙ,
all: ∀x:A. B[x],
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
guard: {T},
so_apply: x[s],
so_lambda: λ2x.t[x],
and: P ∧ Q,
prop: ℙ,
top: Top,
so_apply: x[s1;s2],
so_lambda: λ2x y.t[x; y],
subtype_rel: A ⊆r B,
false: False,
implies: P ⇒ Q,
not: ¬A,
member: t ∈ T,
uimplies: b supposing a,
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
es-interface-empty: es-interface-empty(es;I),
Q-R-pre-preserving: f is Q-R-pre-preserving on P,
inject: Inj(A;B;f),
es-E-interface: E(X),
weak-antecedent-function: Q ←==f== P,
weak-antecedent-surjection: Q ←←= f== P,
es-interface-predicate: {I},
Q-R-glues: g glues Ia:Qa ──f⟶ Ib:Rb
Latex:
\mforall{}[Info:Type]
\mforall{}es:EO+(Info)
\mforall{}[Qa,Rb:E {}\mrightarrow{} E {}\mrightarrow{} \mBbbP{}]. \mforall{}[A,B:Type].
\mforall{}Ia:EClass(A). \mforall{}Ib:EClass(B). \mforall{}f,g:Top.
(g glues Ia:Qa {}{}f{}\mrightarrow{} Ib:Rb) supposing
(es-interface-empty(es;Ib) and
es-interface-empty(es;Ia))
Date html generated:
2016_05_17-AM-07_50_03
Last ObjectModification:
2015_12_28-PM-11_30_12
Theory : event-ordering
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