(* *)
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-set "baseuri" "cic:/matita/algebra/groups/".
-
include "algebra/monoids.ma".
include "nat/le_arith.ma".
include "datatypes/bool.ma".
f_morph: ∀x,y:G.image(x·y) = image x · image y
}.
-notation "hvbox(f˜ x)" with precedence 79
+notation "hvbox(f\tilde x)" with precedence 79
for @{ 'morimage $f $x }.
interpretation "Morphism image" 'morimage f x =
definition member_of_subgroup ≝
λG.λH:subgroup G.λx:G.∃y.x=y \sub H.
-notation "hvbox(x break ∈ H)" with precedence 79
+notation "hvbox(x break \in H)" with precedence 79
for @{ 'member_of $x $H }.
-notation "hvbox(x break ∉ H)" with precedence 79
+notation "hvbox(x break \notin H)" with precedence 79
for @{ 'not_member_of $x $H }.
interpretation "Member of subgroup" 'member_of x H =
λG.λC,C':left_coset G.
∀x.¬(((element ? C)·x \sub (subgrp ? C)) ∈ C').
-notation "hvbox(a break ∥ b)"
+notation "hvbox(a break \par b)"
non associative with precedence 45
for @{ 'disjoint $a $b }.