Nuprl Lemma : Q-R-glues-property
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[Qa,Rb:E ─→ E ─→ ℙ]. ∀[A,B:Type]. ∀[Ia:EClass(A)]. ∀[Ib:EClass(B)]. ∀[f:E(Ia) ─→ B].
∀[g:E(Ib) ─→ E].
g ∈ E(Ib) ─→ E(Ia) supposing g glues Ia:Qa ──f─→ Ib:Rb
Proof
Definitions occuring in Statement :
Q-R-glues: g glues Ia:Qa ──f─→ Ib:Rb,
es-E-interface: E(X),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
function: x:A ─→ B[x],
universe: Type
Lemmas :
weak-antecedent-surjection-property,
es-interface-predicate_wf,
interface_predicate_set_lemma,
Q-R-glues_wf,
es-E-interface_wf,
es-interface-subtype_rel2,
es-E_wf,
event-ordering+_subtype,
top_wf,
eclass_wf,
event-ordering+_wf
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:E(Ia) {}\mrightarrow{} B]. \mforall{}[g:E(Ib) {}\mrightarrow{} E].
g \mmember{} E(Ib) {}\mrightarrow{} E(Ia) supposing g glues Ia:Qa {}{}f{}\mrightarrow{} Ib:Rb
Date html generated:
2015_07_21-PM-04_08_02
Last ObjectModification:
2015_01_27-PM-05_42_13
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