Step
*
1
of Lemma
oal_umap_char
1. s : LOSet
2. g : AbDMon
3. h : AbMon
4. f : |s| ⟶ MonHom(g,h)
⊢ (λps:|oal(s;g)|. msFor{h} k ∈ dom(ps)
(f k (ps[k]))) = !v:|oal(s;g)| ⟶ |h|
(IsMonHom{oal_mon(s;g),h}(v)
∧ (∀j:|s|. ((f j) = (v o (λw.inj(j,w))) ∈ (|g| ⟶ |h|))))
BY
{ % Useful to have properties of f available.
Should be able to do this without explicit introduction %
((Assert ∀k:|s|. IsMonHom{g,h}(f k)
THENA D 0) THENA Auto) }
1
1. s : LOSet
2. g : AbDMon
3. h : AbMon
4. f : |s| ⟶ MonHom(g,h)
5. k : |s|
⊢ IsMonHom{g,h}(f k)
2
1. s : LOSet
2. g : AbDMon
3. h : AbMon
4. f : |s| ⟶ MonHom(g,h)
5. ∀k:|s|. IsMonHom{g,h}(f k)
⊢ (λps:|oal(s;g)|. msFor{h} k ∈ dom(ps)
(f k (ps[k]))) = !v:|oal(s;g)| ⟶ |h|
(IsMonHom{oal_mon(s;g),h}(v)
∧ (∀j:|s|. ((f j) = (v o (λw.inj(j,w))) ∈ (|g| ⟶ |h|))))
Latex:
Latex:
1. s : LOSet
2. g : AbDMon
3. h : AbMon
4. f : |s| {}\mrightarrow{} MonHom(g,h)
\mvdash{} (\mlambda{}ps:|oal(s;g)|. msFor\{h\} k \mmember{} dom(ps)
(f k (ps[k]))) = !v:|oal(s;g)| {}\mrightarrow{} |h|
(IsMonHom\{oal\_mon(s;g),h\}(v)
\mwedge{} (\mforall{}j:|s|. ((f j) = (v o (\mlambda{}w.inj(j,w))))))
By
Latex:
\% Useful to have properties of f available.
Should be able to do this without explicit introduction \%
((Assert \mforall{}k:|s|. IsMonHom\{g,h\}(f k)
THENA D 0) THENA Auto)
Home
Index