Theorem: Digraph.Walk.coe_support_append' (GraphProjects/DigraphConnectivity.lean)

State before:
V : Type u
V' : Type v
V'' : Type w
G : Digraph V
G' : Digraph V'
G'' : Digraph V''
inst✝ : DecidableEq V
u v w : V
p : Walk G u v
p' : Walk G v w
⊢ ↑(support (append p p')) = ↑(support p) + ↑(support p') - {v}
Tactic:
rw [support_append, ← Multiset.coe_add]
State after:
V : Type u
V' : Type v
V'' : Type w
G : Digraph V
G' : Digraph V'
G'' : Digraph V''
inst✝ : DecidableEq V
u v w : V
p : Walk G u v
p' : Walk G v w
⊢ ↑(support p) + ↑(List.tail (support p')) = ↑(support p) + ↑(support p') - {v}

State before:
V : Type u
V' : Type v
V'' : Type w
G : Digraph V
G' : Digraph V'
G'' : Digraph V''
inst✝ : DecidableEq V
u v w : V
p : Walk G u v
p' : Walk G v w
⊢ ↑(support p) + ↑(List.tail (support p')) = ↑(support p) + ↑(support p') - {v}
Tactic:
simp only [coe_support]
State after:
V : Type u
V' : Type v
V'' : Type w
G : Digraph V
G' : Digraph V'
G'' : Digraph V''
inst✝ : DecidableEq V
u v w : V
p : Walk G u v
p' : Walk G v w
⊢ {u} + ↑(List.tail (support p)) + ↑(List.tail (support p')) =
    {u} + ↑(List.tail (support p)) + ({v} + ↑(List.tail (support p'))) - {v}

State before:
V : Type u
V' : Type v
V'' : Type w
G : Digraph V
G' : Digraph V'
G'' : Digraph V''
inst✝ : DecidableEq V
u v w : V
p : Walk G u v
p' : Walk G v w
⊢ {u} + ↑(List.tail (support p)) + ↑(List.tail (support p')) =
    {u} + ↑(List.tail (support p)) + ({v} + ↑(List.tail (support p'))) - {v}
Tactic:
rw [add_comm ({v} : Multiset V)]
State after:
V : Type u
V' : Type v
V'' : Type w
G : Digraph V
G' : Digraph V'
G'' : Digraph V''
inst✝ : DecidableEq V
u v w : V
p : Walk G u v
p' : Walk G v w
⊢ {u} + ↑(List.tail (support p)) + ↑(List.tail (support p')) =
    {u} + ↑(List.tail (support p)) + (↑(List.tail (support p')) + {v}) - {v}

State before:
V : Type u
V' : Type v
V'' : Type w
G : Digraph V
G' : Digraph V'
G'' : Digraph V''
inst✝ : DecidableEq V
u v w : V
p : Walk G u v
p' : Walk G v w
⊢ {u} + ↑(List.tail (support p)) + ↑(List.tail (support p')) =
    {u} + ↑(List.tail (support p)) + (↑(List.tail (support p')) + {v}) - {v}
Tactic:
simp only [← add_assoc, add_tsub_cancel_right]
State after:
no goals