case is_rename.const_eq
t₁ : term,
c₁ c₂ : string,
h₁ h₂ : is_rename (term.const c₁) c₁ c₂ (term.const c₂)
⊢ term.const c₂ = term.const c₂
case is_rename.const_ne
t₁ : term,
c₁ c₂ : string,
h₁ : is_rename (term.const c₁) c₁ c₂ (term.const c₂),
h₂_hne : c₁ ≠ c₁,
h₂ : is_rename (term.const c₁) c₁ c₂ (term.const c₁)
⊢ term.const c₂ = term.const c₁
case is_rename.const_eq
t₁ : term,
c₁ c₂ : string,
h₁_hne : c₁ ≠ c₁,
h₁ : is_rename (term.const c₁) c₁ c₂ (term.const c₁),
h₂ : is_rename (term.const c₁) c₁ c₂ (term.const c₂)
⊢ term.const c₁ = term.const c₂
case is_rename.const_ne
t₁ : term,
c₁ c₁' c₂ : string,
h₁_hne : c₁ ≠ c₁',
h₁ : is_rename (term.const c₁) c₁' c₂ (term.const c₁),
h₂_hne : c₁ ≠ c₁',
h₂ : is_rename (term.const c₁) c₁' c₂ (term.const c₁)
⊢ term.const c₁ = term.const c₁
t₁ : term,
fn : string,
ts : list term,
ih :
  ∀ (ts₂ ts₂' : list term) (c₁ c₂ : string),
    is_rename_lst ts c₁ c₂ ts₂ → is_rename_lst ts c₁ c₂ ts₂' → ts₂ = ts₂',
c₁ c₂ : string,
h₁_ts₂ : list term,
h₁_h₁ : is_rename_lst ts c₁ c₂ h₁_ts₂,
h₁ : is_rename (term.app fn ts) c₁ c₂ (term.app fn h₁_ts₂),
h₂_ts₂ : list term,
h₂_h₁ : is_rename_lst ts c₁ c₂ h₂_ts₂,
h₂ : is_rename (term.app fn ts) c₁ c₂ (term.app fn h₂_ts₂)
⊢ term.app fn h₁_ts₂ = term.app fn h₂_ts₂