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