Step
*
of Lemma
mset_for_of_op
∀g:IAbMonoid. ∀s:DSet. ∀e,f:|s| ⟶ |g|. ∀a:MSet{s}.
((msFor{g} x ∈ a. (e[x] * f[x])) = ((msFor{g} x ∈ a. e[x]) * (msFor{g} x ∈ a. f[x])) ∈ |g|)
BY
{ ((CDToVarThen `f' (\i.RW mset_elimC 0)) THENA Auto) }
1
1. g : IAbMonoid@i'
2. s : DSet@i'
3. e : |s| ⟶ |g|@i
4. f : |s| ⟶ |g|@i
⊢ ∀a:|s| List. ((For{g} x ∈ a. (e[x] * f[x])) = ((For{g} x ∈ a. e[x]) * (For{g} x ∈ a. f[x])) ∈ |g|)
Latex:
Latex:
\mforall{}g:IAbMonoid. \mforall{}s:DSet. \mforall{}e,f:|s| {}\mrightarrow{} |g|. \mforall{}a:MSet\{s\}.
((msFor\{g\} x \mmember{} a. (e[x] * f[x])) = ((msFor\{g\} x \mmember{} a. e[x]) * (msFor\{g\} x \mmember{} a. f[x])))
By
Latex:
((CDToVarThen `f' (\mbackslash{}i.RW mset\_elimC 0)) THENA Auto)
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