Theorem: Digraph.Walk.length_takeUntil_le (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 v w
h : u ∈ support p
⊢ length (takeUntil p u h) ≤ length p
Tactic:
have := congr_arg Walk.length (p.take_spec h)
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 v w
h : u ∈ support p
this : length (append (takeUntil p u h) (dropUntil p u h)) = length p
⊢ length (takeUntil p u h) ≤ length p

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 v w
h : u ∈ support p
this : length (append (takeUntil p u h) (dropUntil p u h)) = length p
⊢ length (takeUntil p u h) ≤ length p
Tactic:
rw [length_append] at this
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 v w
h : u ∈ support p
this : length (takeUntil p u h) + length (dropUntil p u h) = length p
⊢ length (takeUntil p u h) ≤ length p

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 v w
h : u ∈ support p
this : length (takeUntil p u h) + length (dropUntil p u h) = length p
⊢ length (takeUntil p u h) ≤ length p
Tactic:
exact Nat.le.intro this
State after:
no goals