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Step * 1 of Lemma fg-lift_wf


1. X : Type
2. G : Group{i}
3. f : X ⟶ |G|
⊢ fg-lift(G;f) ∈ MonHom(free-group(X),G)
BY
{ (Unfold `fg-lift` 0
   THEN (MemTypeCD THEN Auto)
   THEN BLemma `grp_hom_formation` 
   THEN Auto
   THEN RepUR ``free-group`` 0
   THEN RepUR ``free-group`` -2
   THEN RepUR ``free-group`` -1) }

1
1. X : Type
2. G : Group{i}
3. f : X ⟶ |G|
4. a : free-word(X)
5. b : free-word(X)
⊢ fg-hom(G;f;a + b) = (fg-hom(G;f;a) * fg-hom(G;f;b)) ∈ |G|

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Latex:

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Latex:

1.  X  :  Type
2.  G  :  Group\{i\}
3.  f  :  X  {}\mrightarrow{}  |G|
\mvdash{}  fg-lift(G;f)  \mmember{}  MonHom(free-group(X),G)


By

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Latex:
(Unfold  `fg-lift`  0
  THEN  (MemTypeCD  THEN  Auto)
  THEN  BLemma  `grp\_hom\_formation` 
  THEN  Auto
  THEN  RepUR  ``free-group``  0
  THEN  RepUR  ``free-group``  -2
  THEN  RepUR  ``free-group``  -1)

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