Theorem: serial_of_refl (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
⊢ Serial rel
Tactic:
rintro w
State after:
α : Type u
rel : α → α → Prop
hRefl : Reflexive rel
hSymm : Symmetric rel
hSerial : Serial rel
hTrans : Transitive rel
hEucl : Euclidean rel
w : α
⊢ ∃ w₂, rel w w₂

State before:
α : Type u
rel : α → α → Prop
hRefl : Reflexive rel
hSymm : Symmetric rel
hSerial : Serial rel
hTrans : Transitive rel
hEucl : Euclidean rel
w : α
⊢ ∃ w₂, rel w w₂
Tactic:
existsi w
State after:
α : Type u
rel : α → α → Prop
hRefl : Reflexive rel
hSymm : Symmetric rel
hSerial : Serial rel
hTrans : Transitive rel
hEucl : Euclidean rel
w : α
⊢ rel w w

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