Theorem: IMOSL.IMO2012A5.PeriodEquiv.mul_left_equiv (IMOSLLean4/IMO2012/A5/A5General/A5Periodic.lean)

State before:
R : Type u_1
S : Type u_2
inst✝² : Ring R
inst✝¹ : NonAssocRing S
inst✝ : NoZeroDivisors S
f : R → S
hf : NontrivialGood f
c d : R
h : (PeriodEquiv f) c d
a : R
⊢ (PeriodEquiv f) (a * c) (a * d)
Tactic:
rw [iff_sub, ← mul_sub]
State after:
R : Type u_1
S : Type u_2
inst✝² : Ring R
inst✝¹ : NonAssocRing S
inst✝ : NoZeroDivisors S
f : R → S
hf : NontrivialGood f
c d : R
h : (PeriodEquiv f) c d
a : R
⊢ (PeriodEquiv f) (a * (c - d)) 0

State before:
R : Type u_1
S : Type u_2
inst✝² : Ring R
inst✝¹ : NonAssocRing S
inst✝ : NoZeroDivisors S
f : R → S
hf : NontrivialGood f
c d : R
h : (PeriodEquiv f) c d
a : R
⊢ (PeriodEquiv f) (a * (c - d)) 0
Tactic:
exact mul_left_equiv_zero hf (iff_sub.mp h) a
State after:
no goals