Theorem: Lean4Axiomatic.Natural.le_from_lt (Lean4Axiomatic/Natural/Order.lean)

State before:
ℕ : Type
inst✝³ : Core ℕ
inst✝² : Induction ℕ
inst✝¹ : Addition ℕ
inst✝ : Sign ℕ
order_inst : Order ℕ
n m : ℕ
⊢ n < m → n ≤ m
Tactic:
intro (_ : n < m)
State after:
ℕ : Type
inst✝³ : Core ℕ
inst✝² : Induction ℕ
inst✝¹ : Addition ℕ
inst✝ : Sign ℕ
order_inst : Order ℕ
n m : ℕ
x✝ : n < m
⊢ n ≤ m

State before:
ℕ : Type
inst✝³ : Core ℕ
inst✝² : Induction ℕ
inst✝¹ : Addition ℕ
inst✝ : Sign ℕ
order_inst : Order ℕ
n m : ℕ
x✝ : n < m
⊢ n ≤ m
Tactic:
have ⟨(_ : n ≤ m), _⟩ := lt_defn.mp ‹n < m›
State after:
ℕ : Type
inst✝³ : Core ℕ
inst✝² : Induction ℕ
inst✝¹ : Addition ℕ
inst✝ : Sign ℕ
order_inst : Order ℕ
n m : ℕ
x✝ : n < m
left✝ : n ≤ m
right✝ : n ≄ m
⊢ n ≤ m

State before:
ℕ : Type
inst✝³ : Core ℕ
inst✝² : Induction ℕ
inst✝¹ : Addition ℕ
inst✝ : Sign ℕ
order_inst : Order ℕ
n m : ℕ
x✝ : n < m
left✝ : n ≤ m
right✝ : n ≄ m
⊢ n ≤ m
Tactic:
exact ‹n ≤ m›
State after:
no goals