English
There is a bijection between formulas with constants and formulas with an extra free variable γ, namely an equivalence L[[γ]].BoundedFormula α n ≃ L.BoundedFormula (γ ⊕ α) n, given by mapTermRelEquiv with Term.constantsVarsEquivLeft and sumEmpty.
Русский
Существует биекция между формулами с константами и формулами с дополнительной свободной переменной γ: Equiv between L[[γ]].BoundedFormula α n и L.BoundedFormula (γ ⊕ α) n через mapTermRelEquiv с Term.constantsVarsEquivLeft и sumEmpty.
LaTeX
$$$\\text{constantsVarsEquiv} : L[[\\gamma]].BoundedFormula \\alpha n \\simeq L.BoundedFormula (\\gamma \\oplus \\alpha) n$$$
Lean4
/-- A bijection sending formulas with constants to formulas with extra free variables. -/
def constantsVarsEquiv : L[[γ]].BoundedFormula α n ≃ L.BoundedFormula (γ ⊕ α) n :=
mapTermRelEquiv (fun _ => Term.constantsVarsEquivLeft) fun _ => Equiv.sumEmpty _ _
