Theorem: Imo2019P2.Imo2019q2Cfg.cospherical_A₁Q₁CA₂ (Compfiles/Imo2019P2.lean)

State before:
V : Type u_1
Pt : Type u_2
inst✝³ : NormedAddCommGroup V
inst✝² : InnerProductSpace ℝ V
inst✝¹ : MetricSpace Pt
inst✝ : NormedAddTorsor V Pt
hd2 : Fact (finrank ℝ V = 2)
cfg : Imo2019q2Cfg V Pt
⊢ Cospherical {cfg.A₁, cfg.Q₁, cfg.C, cfg.A₂}
Tactic:
haveI := someOrientation V
State after:
V : Type u_1
Pt : Type u_2
inst✝³ : NormedAddCommGroup V
inst✝² : InnerProductSpace ℝ V
inst✝¹ : MetricSpace Pt
inst✝ : NormedAddTorsor V Pt
hd2 : Fact (finrank ℝ V = 2)
cfg : Imo2019q2Cfg V Pt
this : Module.Oriented ℝ V (Fin 2)
⊢ Cospherical {cfg.A₁, cfg.Q₁, cfg.C, cfg.A₂}

State before:
V : Type u_1
Pt : Type u_2
inst✝³ : NormedAddCommGroup V
inst✝² : InnerProductSpace ℝ V
inst✝¹ : MetricSpace Pt
inst✝ : NormedAddTorsor V Pt
hd2 : Fact (finrank ℝ V = 2)
cfg : Imo2019q2Cfg V Pt
this : Module.Oriented ℝ V (Fin 2)
⊢ Cospherical {cfg.A₁, cfg.Q₁, cfg.C, cfg.A₂}
Tactic:
rw [Set.insert_comm cfg.Q₁, Set.insert_comm cfg.A₁, Set.pair_comm, Set.insert_comm cfg.A₁,
  Set.pair_comm]
State after:
V : Type u_1
Pt : Type u_2
inst✝³ : NormedAddCommGroup V
inst✝² : InnerProductSpace ℝ V
inst✝¹ : MetricSpace Pt
inst✝ : NormedAddTorsor V Pt
hd2 : Fact (finrank ℝ V = 2)
cfg : Imo2019q2Cfg V Pt
this : Module.Oriented ℝ V (Fin 2)
⊢ Cospherical {cfg.C, cfg.A₂, cfg.Q₁, cfg.A₁}

State before:
V : Type u_1
Pt : Type u_2
inst✝³ : NormedAddCommGroup V
inst✝² : InnerProductSpace ℝ V
inst✝¹ : MetricSpace Pt
inst✝ : NormedAddTorsor V Pt
hd2 : Fact (finrank ℝ V = 2)
cfg : Imo2019q2Cfg V Pt
this : Module.Oriented ℝ V (Fin 2)
⊢ Cospherical {cfg.C, cfg.A₂, cfg.Q₁, cfg.A₁}
Tactic:
exact cospherical_of_two_zsmul_oangle_eq_of_not_collinear
  cfg.two_zsmul_oangle_CA₂A₁_eq_two_zsmul_oangle_CQ₁A₁ cfg.not_collinear_CA₂A₁
State after:
no goals