Nuprl Lemma : conditional_wf-interface
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[A,B:Type]. ∀[Ia1,Ia2:EClass(A)]. ∀[Ib1,Ib2:EClass(B)]. ∀[g1:E(Ib1) ─→ E(Ia1)].
∀[g2:E(Ib2) ─→ E(Ia2)].
([{Ib1}? g1 : g2] ∈ E([Ib1?Ib2]) ─→ E([Ia1?Ia2]))
Proof
Definitions occuring in Statement :
es-E-interface: E(X),
es-interface-predicate: {I},
cond-class: [X?Y],
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
conditional: [P? f : g],
uall: ∀[x:A]. B[x],
member: t ∈ T,
lambda: λx.A[x],
function: x:A ─→ B[x],
universe: Type,
bool-decider: bool-decider(b)
Lemmas :
in-eclass_wf,
es-interface-subtype_rel2,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
top_wf,
cond-class_wf,
assert_wf,
not_wf,
branch_wf2,
bool-decider_wf,
es-E-interface_wf,
es-E-interface-conditional-subtype1,
es-E-interface-conditional-subtype2,
is-cond-class
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[A,B:Type]. \mforall{}[Ia1,Ia2:EClass(A)]. \mforall{}[Ib1,Ib2:EClass(B)].
\mforall{}[g1:E(Ib1) {}\mrightarrow{} E(Ia1)]. \mforall{}[g2:E(Ib2) {}\mrightarrow{} E(Ia2)].
([\{Ib1\}? g1 : g2] \mmember{} E([Ib1?Ib2]) {}\mrightarrow{} E([Ia1?Ia2]))
Date html generated:
2015_07_21-PM-04_07_12
Last ObjectModification:
2015_01_27-PM-05_50_28
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