Theorem: Digraph.Walk.takeUntil_copy (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' w' : V
p : Walk G v w
hv : v = v'
hw : w = w'
h : u ∈ support (Walk.copy p hv hw)
⊢ u ∈ support p
Tactic:
subst_vars
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 (Walk.copy p (_ : v' = v') (_ : w' = w'))
⊢ u ∈ support 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 (Walk.copy p (_ : v' = v') (_ : w' = w'))
⊢ u ∈ support p
Tactic:
exact h
State after:
no goals

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' w' : V
p : Walk G v w
hv : v = v'
hw : w = w'
h : u ∈ support (Walk.copy p hv hw)
⊢ takeUntil (Walk.copy p hv hw) u h = Walk.copy (takeUntil p u (_ : u ∈ support p)) hv (_ : u = u)
Tactic:
subst_vars
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 (Walk.copy p (_ : v' = v') (_ : w' = w'))
⊢ takeUntil (Walk.copy p (_ : v' = v') (_ : w' = w')) u h =
    Walk.copy (takeUntil p u (_ : u ∈ support p)) (_ : v' = v') (_ : u = u)

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 (Walk.copy p (_ : v' = v') (_ : w' = w'))
⊢ takeUntil (Walk.copy p (_ : v' = v') (_ : w' = w')) u h =
    Walk.copy (takeUntil p u (_ : u ∈ support p)) (_ : v' = v') (_ : u = u)
Tactic:
rfl
State after:
no goals