+If <code>φ</code> is a natural transformation from `F` to `M(1C)` and <code>γ</code> is <code>(φ G')</code>, that is, a natural transformation from `FG'` to `MG'`, then we can extend (iii.1) as follows:
+
+<pre>
+ γ = (φ G')
+ = ((unit <=< φ) G')
+ = (((join 1C) -v- (M unit) -v- φ) G')
+ = (((join 1C) G') -v- ((M unit) G') -v- (φ G'))
+ = ((join (1C G')) -v- (M (unit G')) -v- γ)
+ = ((join G') -v- (M (unit G')) -v- γ)
+ since (unit G') is a natural transformation to MG',
+ this satisfies the definition for <=<:
+ = (unit G') <=< γ
+</pre>
+
+where as we said <code>γ</code> is a natural transformation from some `FG'` to `MG'`.
+
+Similarly, if <code>ρ</code> is a natural transformation from `1C` to `MR'`, and <code>γ</code> is <code>(ρ G)</code>, that is, a natural transformation from `G` to `MR'G`, then we can extend (iii.2) as follows:
+
+<pre>
+ γ = (ρ G)
+ = ((ρ <=< unit) G)
+ = (((join R') -v- (M ρ) -v- unit) G)
+ = (((join R') G) -v- ((M ρ) G) -v- (unit G))
+ = ((join (R'G)) -v- (M (ρ G)) -v- (unit G))
+ since γ = (ρ G) is a natural transformation to MR'G,
+ this satisfies the definition <=<:
+ = γ <=< (unit G)
+</pre>
+
+where as we said <code>γ</code> is a natural transformation from `G` to some `MR'G`.
+
+Summarizing then, the monad laws can be expressed as:
+
+<pre>
+ For all ρ, γ, φ in T for which ρ <=< γ and γ <=< φ are defined: