Theorem: Digraph.Walk.toDeleteEdges_copy (GraphProjects/DigraphConnectivity.lean)

State before:
V : Type u
V' : Type v
V'' : Type w
G : Digraph V
G' : Digraph V'
G'' : Digraph V''
u v u' v' : V
s : Set (V × V)
p : Walk G u v
hu : u = u'
hv : v = v'
h : ∀ (e : V × V), e ∈ edges (Walk.copy p hu hv) → ¬e ∈ s
⊢ ∀ (e : V × V), e ∈ edges p → ¬e ∈ s
Tactic:
subst_vars
State after:
V : Type u
V' : Type v
V'' : Type w
G : Digraph V
G' : Digraph V'
G'' : Digraph V''
u' v' : V
s : Set (V × V)
p : Walk G u' v'
h : ∀ (e : V × V), e ∈ edges (Walk.copy p (_ : u' = u') (_ : v' = v')) → ¬e ∈ s
⊢ ∀ (e : V × V), e ∈ edges p → ¬e ∈ s

State before:
V : Type u
V' : Type v
V'' : Type w
G : Digraph V
G' : Digraph V'
G'' : Digraph V''
u' v' : V
s : Set (V × V)
p : Walk G u' v'
h : ∀ (e : V × V), e ∈ edges (Walk.copy p (_ : u' = u') (_ : v' = v')) → ¬e ∈ s
⊢ ∀ (e : V × V), e ∈ edges p → ¬e ∈ s
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''
u v u' v' : V
s : Set (V × V)
p : Walk G u v
hu : u = u'
hv : v = v'
h : ∀ (e : V × V), e ∈ edges (Walk.copy p hu hv) → ¬e ∈ s
⊢ toDeleteEdges s (Walk.copy p hu hv) h = Walk.copy (toDeleteEdges s p (_ : ∀ (e : V × V), e ∈ edges p → ¬e ∈ s)) hu hv
Tactic:
subst_vars
State after:
V : Type u
V' : Type v
V'' : Type w
G : Digraph V
G' : Digraph V'
G'' : Digraph V''
u' v' : V
s : Set (V × V)
p : Walk G u' v'
h : ∀ (e : V × V), e ∈ edges (Walk.copy p (_ : u' = u') (_ : v' = v')) → ¬e ∈ s
⊢ toDeleteEdges s (Walk.copy p (_ : u' = u') (_ : v' = v')) h =
    Walk.copy (toDeleteEdges s p (_ : ∀ (e : V × V), e ∈ edges p → ¬e ∈ s)) (_ : u' = u') (_ : v' = v')

State before:
V : Type u
V' : Type v
V'' : Type w
G : Digraph V
G' : Digraph V'
G'' : Digraph V''
u' v' : V
s : Set (V × V)
p : Walk G u' v'
h : ∀ (e : V × V), e ∈ edges (Walk.copy p (_ : u' = u') (_ : v' = v')) → ¬e ∈ s
⊢ toDeleteEdges s (Walk.copy p (_ : u' = u') (_ : v' = v')) h =
    Walk.copy (toDeleteEdges s p (_ : ∀ (e : V × V), e ∈ edges p → ¬e ∈ s)) (_ : u' = u') (_ : v' = v')
Tactic:
rfl
State after:
no goals