imo.imo1977_q6
⟷
Archive.Imo.Imo1977Q6
The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.
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mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -3,7 +3,7 @@ Copyright (c) 2021 Tian Chen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tian Chen
-/
-import Data.Pnat.Basic
+import Data.PNat.Basic
#align_import imo.imo1977_q6 from "leanprover-community/mathlib"@"08b081ea92d80e3a41f899eea36ef6d56e0f1db0"
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -3,7 +3,7 @@ Copyright (c) 2021 Tian Chen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tian Chen
-/
-import Mathbin.Data.Pnat.Basic
+import Data.Pnat.Basic
#align_import imo.imo1977_q6 from "leanprover-community/mathlib"@"08b081ea92d80e3a41f899eea36ef6d56e0f1db0"
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,14 +2,11 @@
Copyright (c) 2021 Tian Chen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tian Chen
-
-! This file was ported from Lean 3 source module imo.imo1977_q6
-! leanprover-community/mathlib commit 08b081ea92d80e3a41f899eea36ef6d56e0f1db0
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.Data.Pnat.Basic
+#align_import imo.imo1977_q6 from "leanprover-community/mathlib"@"08b081ea92d80e3a41f899eea36ef6d56e0f1db0"
+
/-!
# IMO 1977 Q6
mathlib commit https://github.com/leanprover-community/mathlib/commit/bf2428c9486c407ca38b5b3fb10b87dad0bc99fa
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tian Chen
! This file was ported from Lean 3 source module imo.imo1977_q6
-! leanprover-community/mathlib commit 308826471968962c6b59c7ff82a22757386603e3
+! leanprover-community/mathlib commit 08b081ea92d80e3a41f899eea36ef6d56e0f1db0
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
@@ -13,6 +13,9 @@ import Mathbin.Data.Pnat.Basic
/-!
# IMO 1977 Q6
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
Suppose `f : ℕ+ → ℕ+` satisfies `f(f(n)) < f(n + 1)` for all `n`.
Prove that `f(n) = n` for all `n`.
mathlib commit https://github.com/leanprover-community/mathlib/commit/7e5137f579de09a059a5ce98f364a04e221aabf0
@@ -34,7 +34,6 @@ theorem imo1977_q6_nat (f : ℕ → ℕ) (h : ∀ n, f (f n) < f (n + 1)) : ∀
calc
k ≤ f (f (n - 1)) := h_ind _ (h_ind (n - 1) (le_tsub_of_add_le_right hk))
_ < f n := tsub_add_cancel_of_le (le_trans (Nat.succ_le_succ (Nat.zero_le _)) hk) ▸ h _
-
have hf : ∀ n, n ≤ f n := fun n => h' n n rfl.le
have hf_mono : StrictMono f := strictMono_nat_of_lt_succ fun _ => lt_of_le_of_lt (hf _) (h _)
intro
mathlib commit https://github.com/leanprover-community/mathlib/commit/a3209ddf94136d36e5e5c624b10b2a347cc9d090
@@ -2,14 +2,11 @@
Copyright (c) 2021 Tian Chen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tian Chen
-
-! This file was ported from Lean 3 source module imo.imo1977_q6
-! leanprover-community/mathlib commit 308826471968962c6b59c7ff82a22757386603e3
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.Data.PNat.Basic
+#align_import imo.imo1977_q6 from "leanprover-community/mathlib"@"308826471968962c6b59c7ff82a22757386603e3"
+
/-!
# IMO 1977 Q6