have : Multiset.count a0 (a ::ₘ M) = Multiset.count a0 X + 1 := by subst_eqs; rw [mul_cons_trivial] at H; simp_all
α : Type u
inst✝¹ : DecidableEq α
inst✝ : LT α
a a0 : α
M X : Multiset α
H✝ : a ::ₘ M = X + {a0}
hyp : ¬a = a0
a0_a : a0 ≠ a
b : α
H : Multiset.count a0 (a ::ₘ M) = Multiset.count a0 (X + {a0})
ba : ¬b = a
ba0 : b = a0
this : Multiset.count a0 ((a ::ₘ M).erase a) = Multiset.count a0 ((a ::ₘ M).erase a)
⊢ Multiset.count a0 M = (Multiset.count a0 X + if a0 = a0 then 1 else 0) - if a0 = a then 1 else 0
α : Type u
inst✝¹ : DecidableEq α
inst✝ : LT α
a a0 : α
M X : Multiset α
H✝ : a ::ₘ M = X + {a0}
hyp : ¬a = a0
a0_a : a0 ≠ a
b : α
H : Multiset.count a0 (a ::ₘ M) = Multiset.count a0 (X + {a0})
ba : ¬b = a
ba0 : b = a0
this✝ : Multiset.count a0 ((a ::ₘ M).erase a) = Multiset.count a0 ((a ::ₘ M).erase a)
this : Multiset.count a0 (a ::ₘ M) = Multiset.count a0 X + 1
⊢ Multiset.count a0 M = (Multiset.count a0 X + if a0 = a0 then 1 else 0) - if a0 = a then 1 else 0