theorem
proved
term proof
nno_universal_uniqueness
show as:
view Lean formalization →
formal statement (Lean)
82theorem nno_universal_uniqueness {α : Type*} (base : α) (step : α → α)
83 (f g : LogicNat → α)
84 (hf_zero : f LogicNat.zero = base)
85 (hf_succ : ∀ n, f (LogicNat.succ n) = step (f n))
86 (hg_zero : g LogicNat.zero = base)
87 (hg_succ : ∀ n, g (LogicNat.succ n) = step (g n)) :
88 f = g := by
proof body
Term-mode proof.
89 funext n
90 induction n with
91 | identity =>
92 rw [show LogicNat.identity = LogicNat.zero from rfl, hf_zero, hg_zero]
93 | step k ih =>
94 rw [show LogicNat.step k = LogicNat.succ k from rfl, hf_succ k, hg_succ k, ih]
95
96/-! ## Master cert -/
97