Porting note: `apply` → `induction`

[Pietro Monticone]

Classifies porting notes claiming:

apply → induction

Examples

mathlib4/Mathlib/Data/Polynomial/Eval.lean

Lines 419 to 427 in f0f609c

 @[simp] 
 theorem eval_C_mul : (C a * p).eval x = a * p.eval x := by 
   -- Porting note: `apply` → `induction` 
   induction p using Polynomial.induction_on' with 
   | h_add p q ph qh => 
     simp only [mul_add, eval_add, ph, qh] 
   | h_monomial n b => 
     simp only [mul_assoc, C_mul_monomial, eval_monomial] 
 #align polynomial.eval_C_mul Polynomial.eval_C_mul 

mathlib4/Mathlib/Data/Polynomial/Eval.lean

Lines 467 to 476 in f0f609c

 @[simp] 
 theorem eval_mul_X : (p * X).eval x = p.eval x * x := by 
   -- Porting note: `apply` → `induction` 
   induction p using Polynomial.induction_on' with 
   | h_add p q ph qh => 
     simp only [add_mul, eval_add, ph, qh] 
   | h_monomial n a => 
     simp only [← monomial_one_one_eq_X, monomial_mul_monomial, eval_monomial, mul_one, pow_succ', 
       mul_assoc] 
 #align polynomial.eval_mul_X Polynomial.eval_mul_X 

mathlib4/Mathlib/Data/Polynomial/Eval.lean

Lines 604 to 612 in f0f609c

 @[simp] 
 theorem mul_X_comp : (p * X).comp r = p.comp r * r := by 
   -- Porting note: `apply` → `induction` 
   induction p using Polynomial.induction_on' with 
   | h_add p q hp hq => 
     simp only [hp, hq, add_mul, add_comp] 
   | h_monomial n b => 
     simp only [pow_succ', mul_assoc, monomial_mul_X, monomial_comp] 
 #align polynomial.mul_X_comp Polynomial.mul_X_comp 

mathlib4/Mathlib/Data/Polynomial/Eval.lean

Lines 628 to 636 in f0f609c

 @[simp] 
 theorem C_mul_comp : (C a * p).comp r = C a * p.comp r := by 
   -- Porting note: `apply` → `induction` 
   induction p using Polynomial.induction_on' with 
   | h_add p q hp hq => 
     simp [hp, hq, mul_add] 
   | h_monomial n b => 
     simp [mul_assoc] 
 #align polynomial.C_mul_comp Polynomial.C_mul_comp 

mathlib4/Mathlib/Data/Polynomial/Eval.lean

Lines 628 to 636 in f0f609c

 @[simp] 
 theorem C_mul_comp : (C a * p).comp r = C a * p.comp r := by 
   -- Porting note: `apply` → `induction` 
   induction p using Polynomial.induction_on' with 
   | h_add p q hp hq => 
     simp [hp, hq, mul_add] 
   | h_monomial n b => 
     simp [mul_assoc] 
 #align polynomial.C_mul_comp Polynomial.C_mul_comp 

[Pietro Monticone]

Resolved by #11444.