simp only [← c1_left]
case a
D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
hd : Definition
tl : List Definition
ih :
  Env.WellFormed tl →
    d ∈ tl →
      (Holds D I (Function.updateListITE V d.args (List.map V args)) M tl d.F ↔ Holds D I V M tl (def_ name args))
s1 : Env.Nodup (hd :: tl)
s2 : ∃ E1, hd :: tl = E1 ++ tl
h1_left : ∀ d' ∈ tl, hd.name = d'.name → hd.args.length = d'.args.length → False
h1_right_left : IsMetaVarOrAllDefInEnv tl hd.F
h1_right_right : Env.WellFormed tl
c2 : d ∈ tl
h3_left : name = d.name
h3_right : args.length = d.args.length
c1_left : name = hd.name
c1_right : args.length = hd.args.length
⊢ hd.name = d.name
case a
D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
hd : Definition
tl : List Definition
ih :
  Env.WellFormed tl →
    d ∈ tl →
      (Holds D I (Function.updateListITE V d.args (List.map V args)) M tl d.F ↔ Holds D I V M tl (def_ name args))
s1 : Env.Nodup (hd :: tl)
s2 : ∃ E1, hd :: tl = E1 ++ tl
h1_left : ∀ d' ∈ tl, hd.name = d'.name → hd.args.length = d'.args.length → False
h1_right_left : IsMetaVarOrAllDefInEnv tl hd.F
h1_right_right : Env.WellFormed tl
c2 : d ∈ tl
h3_left : name = d.name
h3_right : args.length = d.args.length
c1_left : name = hd.name
c1_right : args.length = hd.args.length
⊢ name = d.name