Update imo_proofs/imo_1985_p6.lean
Browse files
imo_proofs/imo_1985_p6.lean
CHANGED
@@ -1,6 +1,5 @@
|
|
1 |
import Mathlib
|
2 |
|
3 |
-
set_option linter.unusedVariables.analyzeTactics true
|
4 |
|
5 |
lemma aux_1
|
6 |
(f : β β NNReal β β)
|
@@ -1318,6 +1317,7 @@ lemma imo_1985_p6_nnreal
|
|
1318 |
exact aux_unique f hβ hmoβ hβ x y hxβ hyβ
|
1319 |
|
1320 |
|
|
|
1321 |
theorem imo_1985_p6
|
1322 |
(f : β β β β β)
|
1323 |
(hβ : β x, f 1 x = x)
|
@@ -1325,7 +1325,7 @@ theorem imo_1985_p6
|
|
1325 |
β! a, β n, 0 < n β 0 < f n a β§ f n a < f (n + 1) a β§ f (n + 1) a < 1 := by
|
1326 |
let fn : β β NNReal β β := fun n x => f n x
|
1327 |
have hfnβ: β n x, 0 < n β 0 β€ x β fn n x = f n x := by
|
1328 |
-
exact fun n x
|
1329 |
have hβ: β! a, β (n : β), 0 < n β 0 < fn n a β§ fn n a < fn (n + 1) a β§ fn (n + 1) a < 1 := by
|
1330 |
exact imo_1985_p6_nnreal fn (fun x β¦ hβ βx) fun n x β¦ hβ n βx
|
1331 |
obtain β¨a, haβ, haββ© := hβ
|
@@ -1353,4 +1353,3 @@ theorem imo_1985_p6
|
|
1353 |
exact (hyβ 1 (by decide)).1
|
1354 |
have hyβ
: (0:β) < 0 := by exact lt_trans hyβ hyβ
|
1355 |
exact (lt_self_iff_false 0).mp hyβ
|
1356 |
-
|
|
|
1 |
import Mathlib
|
2 |
|
|
|
3 |
|
4 |
lemma aux_1
|
5 |
(f : β β NNReal β β)
|
|
|
1317 |
exact aux_unique f hβ hmoβ hβ x y hxβ hyβ
|
1318 |
|
1319 |
|
1320 |
+
|
1321 |
theorem imo_1985_p6
|
1322 |
(f : β β β β β)
|
1323 |
(hβ : β x, f 1 x = x)
|
|
|
1325 |
β! a, β n, 0 < n β 0 < f n a β§ f n a < f (n + 1) a β§ f (n + 1) a < 1 := by
|
1326 |
let fn : β β NNReal β β := fun n x => f n x
|
1327 |
have hfnβ: β n x, 0 < n β 0 β€ x β fn n x = f n x := by
|
1328 |
+
exact fun n x _ _ β¦ rfl
|
1329 |
have hβ: β! a, β (n : β), 0 < n β 0 < fn n a β§ fn n a < fn (n + 1) a β§ fn (n + 1) a < 1 := by
|
1330 |
exact imo_1985_p6_nnreal fn (fun x β¦ hβ βx) fun n x β¦ hβ n βx
|
1331 |
obtain β¨a, haβ, haββ© := hβ
|
|
|
1353 |
exact (hyβ 1 (by decide)).1
|
1354 |
have hyβ
: (0:β) < 0 := by exact lt_trans hyβ hyβ
|
1355 |
exact (lt_self_iff_false 0).mp hyβ
|
|