Theorem: LO.Modal.Standard.Kripke.GeachConfluent.dense_def (Logic/Modal/Standard/Kripke/Geach/Definability.lean)

State before:
α : Sort ?u.204827
inst✝ : Inhabited α
F : Frame
⊢ GeachConfluent { i := 0, j := 1, m := 2, n := 0 } F ↔ Dense F.Rel
Tactic:
simp [GeachConfluent, Dense]
State after:
α : Sort ?u.204827
inst✝ : Inhabited α
F : Frame
⊢ (∀ {x y z : F.World}, x = y → x ≺ z → ∃ z_1, y ≺ z_1 ∧ z_1 ≺ z) ↔
    ∀ ⦃w₁ w₂ : F.World⦄, F.Rel w₁ w₂ → ∃ w₃, F.Rel w₁ w₃ ∧ F.Rel w₃ w₂

State before:
α : Sort ?u.204827
inst✝ : Inhabited α
F : Frame
⊢ (∀ {x y z : F.World}, x = y → x ≺ z → ∃ z_1, y ≺ z_1 ∧ z_1 ≺ z) ↔
    ∀ ⦃w₁ w₂ : F.World⦄, F.Rel w₁ w₂ → ∃ w₃, F.Rel w₁ w₃ ∧ F.Rel w₃ w₂
Tactic:
aesop
State after:
no goals