Theorem: symm_of_refl_eucl (Logic/Vorspiel/BinaryRelations.lean)

State before:
α : Type u
rel : α → α → Prop
hRefl : Reflexive rel
hSymm : Symmetric rel
hSerial : Serial rel
hTrans : Transitive rel
hEucl : Euclidean rel
⊢ Symmetric rel
Tactic:
intro w₁ w₂ r₁₂
State after:
α : Type u
rel : α → α → Prop
hRefl : Reflexive rel
hSymm : Symmetric rel
hSerial : Serial rel
hTrans : Transitive rel
hEucl : Euclidean rel
w₁ w₂ : α
r₁₂ : rel w₁ w₂
⊢ rel w₂ w₁

State before:
α : Type u
rel : α → α → Prop
hRefl : Reflexive rel
hSymm : Symmetric rel
hSerial : Serial rel
hTrans : Transitive rel
hEucl : Euclidean rel
w₁ w₂ : α
r₁₂ : rel w₁ w₂
⊢ rel w₂ w₁
Tactic:
exact hEucl (hRefl w₁) r₁₂
State after:
no goals