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
Lemmas :
es-le-before_wf2,
list-subtype-bag,
es-le_wf,
bag_wf,
bag-combine-append-right,
bag-combine_wf,
eo-forward_wf,
member-eo-forward-E,
equal_wf,
Id_wf,
es-loc_wf,
iff_weakening_equal,
bag-combine-append-left,
bag-combine-map,
bag-append_wf,
eclass_wf,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
bag-map_wf
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:
2015_07_21-PM-02_37_48
Last ObjectModification:
2015_02_04-PM-06_20_44
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