constructor
σ : Instantiation
σ' : VarName → VarName
a1_left : ↑σ ∘ σ' = id
a1_right : σ' ∘ ↑σ = id
⊢ σ' ∘ ↑σ = id ∧ ↑σ ∘ σ' = id
case left
σ : Instantiation
σ' : VarName → VarName
a1_left : ↑σ ∘ σ' = id
a1_right : σ' ∘ ↑σ = id
⊢ σ' ∘ ↑σ = id

case right
σ : Instantiation
σ' : VarName → VarName
a1_left : ↑σ ∘ σ' = id
a1_right : σ' ∘ ↑σ = id
⊢ ↑σ ∘ σ' = id