Nuprl Lemma : parallel-class-bind-left
∀[Info,T,S:Type]. ∀[X,Y:EClass(T)]. ∀[Z:T ⟶ EClass(S)].  (X || Y >t> Z[t] = X >t> Z[t] || Y >t> Z[t] ∈ EClass(S))
Proof
Definitions occuring in Statement : 
parallel-class: X || Y
, 
bind-class: X >x> Y[x]
, 
eclass: EClass(A[eo; e])
, 
uall: ∀[x:A]. B[x]
, 
so_apply: x[s]
, 
function: x:A ⟶ B[x]
, 
universe: Type
, 
equal: s = t ∈ T
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
bind-class: X >x> Y[x]
, 
parallel-class: X || Y
, 
eclass: EClass(A[eo; e])
, 
eclass-compose2: eclass-compose2(f;X;Y)
, 
subtype_rel: A ⊆r B
, 
prop: ℙ
, 
uimplies: b supposing a
, 
so_lambda: λ2x.t[x]
, 
all: ∀x:A. B[x]
, 
so_apply: x[s]
, 
so_lambda: λ2x y.t[x; y]
, 
so_apply: x[s1;s2]
, 
implies: P 
⇒ Q
, 
guard: {T}
, 
iff: P 
⇐⇒ Q
, 
and: P ∧ Q
, 
rev_implies: P 
⇐ Q
, 
squash: ↓T
, 
true: True
Latex:
\mforall{}[Info,T,S:Type].  \mforall{}[X,Y:EClass(T)].  \mforall{}[Z:T  {}\mrightarrow{}  EClass(S)].
    (X  ||  Y  >t>  Z[t]  =  X  >t>  Z[t]  ||  Y  >t>  Z[t])
Date html generated:
2016_05_16-PM-02_28_31
Last ObjectModification:
2016_01_17-PM-07_34_51
Theory : event-ordering
Home
Index