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)
Definitions unfolded in proof :
top: Top,
all: ∀x:A. B[x],
uimplies: b supposing a,
so_apply: x[s1;s2],
so_lambda: λ2x y.t[x; y],
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
member: t ∈ T,
conditional: [P? f : g],
prop: ℙ,
es-E-interface: E(X),
es-interface-predicate: {I},
so_lambda: λ2x.t[x],
so_apply: x[s],
false: False,
not: ¬A,
or: P ∨ Q,
implies: P ⇒ Q,
and: P ∧ Q,
iff: P ⇐⇒ Q
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:
2016_05_17-AM-07_47_37
Last ObjectModification:
2015_12_28-PM-11_38_22
Theory : event-ordering
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