Nuprl Lemma : eclass-disju-bind-left
∀[Info,A1,A2,B:Type]. ∀[X1:EClass(A1)]. ∀[X2:EClass(A2)]. ∀[Y1:A1 ⟶ EClass(B)]. ∀[Y2:A2 ⟶ EClass(B)].
(X1 + X2 >x> case x of inl(a1) => Y1[a1] | inr(a2) => Y2[a2] = X1 >x> Y1[x] || X2 >x> Y2[x] ∈ EClass(B))
Proof
Definitions occuring in Statement :
eclass-disju: X + Y,
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],
decide: case b of inl(x) => s[x] | inr(y) => t[y],
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-disju: X + Y,
eclass: EClass(A[eo; e]),
eclass-compose2: eclass-compose2(f;X;Y),
eclass1: (f o X),
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],
implies: P ⇒ Q,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
squash: ↓T,
class-ap: X(e),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
true: True
Latex:
\mforall{}[Info,A1,A2,B:Type]. \mforall{}[X1:EClass(A1)]. \mforall{}[X2:EClass(A2)]. \mforall{}[Y1:A1 {}\mrightarrow{} EClass(B)].
\mforall{}[Y2:A2 {}\mrightarrow{} EClass(B)].
(X1 + X2 >x> case x of inl(a1) => Y1[a1] | inr(a2) => Y2[a2] = X1 >x> Y1[x] || X2 >x> Y2[x])
Date html generated:
2016_05_16-PM-11_42_30
Last ObjectModification:
2016_01_17-PM-07_02_02
Theory : event-ordering
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