Theorem: trans_of_symm_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
⊢ Transitive rel
Tactic:
rintro w₁ w₂ w₃ r₁₂ r₂₃
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 w₃ : α
r₁₂ : rel w₁ w₂
r₂₃ : rel w₂ w₃
⊢ rel w₁ w₃

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 w₃ : α
r₁₂ : rel w₁ w₂
r₂₃ : rel w₂ w₃
⊢ rel w₁ w₃
Tactic:
exact hSymm $ hEucl (hSymm r₁₂) r₂₃
State after:
no goals