# mathlibdocumentation

tactic.rename_var

# Rename bound variable tactic #

This files defines a tactic rename_var whose main purpose is to teach renaming of bound variables.

• rename_var old new renames all bound variables named old to new in the goal.
• rename_var old new at h does the same in hypothesis h.
example (P : ℕ →  ℕ → Prop) (h : ∀ n, ∃ m, P n m) : ∀ l, ∃ m, P l m :=
begin
rename_var n q at h, -- h is now ∀ (q : ℕ), ∃ (m : ℕ), P q m,
rename_var m n, -- goal is now ∀ (l : ℕ), ∃ (n : ℕ), P k n,
exact h -- Lean does not care about those bound variable names
end


## Tags #

teaching, tactic

meta def expr.rename_var (old new : name) :

Rename bound variable old to new in an expr

meta def tactic.rename_var_at_goal (old new : name) :

Rename bound variable old to new in goal

meta def tactic.rename_var_at_hyp (old new : name) (e : expr) :

Rename bound variable old to new in assumption h

rename_var old new renames all bound variables named old to new in the goal. rename_var old new at h does the same in hypothesis h.

rename_var old new renames all bound variables named old to new in the goal. rename_var old new at h does the same in hypothesis h. This is meant for teaching bound variables only. Such a renaming should never be relevant to Lean.

example (P : ℕ →  ℕ → Prop) (h : ∀ n, ∃ m, P n m) : ∀ l, ∃ m, P l m :=
begin
rename_var n q at h, -- h is now ∀ (q : ℕ), ∃ (m : ℕ), P q m,
rename_var m n, -- goal is now ∀ (l : ℕ), ∃ (n : ℕ), P k n,
exact h -- Lean does not care about those bound variable names
end