Theorem: conjugate_mono (FormalisingMathematics2024/Solutions/Section07subgroupsAndHomomorphisms/Sheet1.lean)

State before:
G : Type
inst✝ : Group G
a b : G
H✝ K✝ : Subgroup G
x y z : G
H K : Subgroup G
h : H ≤ K
⊢ conjugate H x ≤ conjugate K x
Tactic:
intro g
State after:
G : Type
inst✝ : Group G
a b : G
H✝ K✝ : Subgroup G
x y z : G
H K : Subgroup G
h : H ≤ K
g : G
⊢ g ∈ conjugate H x → g ∈ conjugate K x

State before:
G : Type
inst✝ : Group G
a b : G
H✝ K✝ : Subgroup G
x y z : G
H K : Subgroup G
h : H ≤ K
g : G
⊢ g ∈ conjugate H x → g ∈ conjugate K x
Tactic:
rintro ⟨t, ht, rfl⟩
State after:
case intro.intro
G : Type
inst✝ : Group G
a b : G
H✝ K✝ : Subgroup G
x y z : G
H K : Subgroup G
h : H ≤ K
t : G
ht : t ∈ H
⊢ x * t * x⁻¹ ∈ conjugate K x

State before:
case intro.intro
G : Type
inst✝ : Group G
a b : G
H✝ K✝ : Subgroup G
x y z : G
H K : Subgroup G
h : H ≤ K
t : G
ht : t ∈ H
⊢ x * t * x⁻¹ ∈ conjugate K x
Tactic:
exact ⟨t, h ht, rfl⟩
State after:
no goals