Merge pull request #501 from Seasawher/auto-update-branch

Author: Seasawher

docs/attributes.md

@@ -1,6 +1,6 @@
 # Attributes
 
-Mathlib version: `ed5b08ca63c16a9533ab652a7c140afca119b817`
+Mathlib version: `acb60b64877e03f0184702506a006f157e37e044`
 
 ## Std.Internal.tree_tac
  simp theorems used by internal DTreeMap lemmas

docs/commands.md

@@ -1,6 +1,6 @@
 # Commands
 
-Mathlib version: `ed5b08ca63c16a9533ab652a7c140afca119b817`
+Mathlib version: `acb60b64877e03f0184702506a006f157e37e044`
 
 ## \#adaptation_note
 Defined in: `adaptationNoteCmd`

docs/options.md

@@ -1,6 +1,6 @@
 # Options
 
-Mathlib version: `ed5b08ca63c16a9533ab652a7c140afca119b817`
+Mathlib version: `acb60b64877e03f0184702506a006f157e37e044`
 
 ## Elab.async
 type: `Bool`

docs/tactics.md

@@ -1,6 +1,6 @@
 # Tactics
 
-Mathlib version: `ed5b08ca63c16a9533ab652a7c140afca119b817`
+Mathlib version: `acb60b64877e03f0184702506a006f157e37e044`
 
 ## \#adaptation_note
 Defined in: `«tactic#adaptation_note_»`
@@ -5791,13 +5791,21 @@ according to the syntax of the expression `x`, if the atoms composing the expres
 numeric lower bounds which can be proved positive/nonnegative/nonzero by `norm_num`.  This tactic
 either closes the goal or fails.
 
+`positivity [t₁, …, tₙ]` first executes `have := t₁; …; have := tₙ` in the current goal,
+then runs `positivity`. This is useful when `positivity` needs derived premises such as `0 < y`
+for division/reciprocal, or `0 ≤ x` for real powers.
+
 Examples:
 ```lean
 example {a : ℤ} (ha : 3 < a) : 0 ≤ a ^ 3 + a := by positivity
 
 example {a : ℤ} (ha : 1 < a) : 0 < |(3:ℤ) + a| := by positivity
 
 example {b : ℤ} : 0 ≤ max (-3) (b ^ 2) := by positivity
+
+example {a b c d : ℝ} (hab : 0 < a * b) (hb : 0 ≤ b) (hcd : c < d) :
+    0 < a ^ c + 1 / (d - c) := by
+  positivity [sub_pos_of_lt hcd, pos_of_mul_pos_left hab hb]
 ```
 
 ## pull

lake-manifest.json

@@ -5,7 +5,7 @@
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-   "rev": "ed5b08ca63c16a9533ab652a7c140afca119b817",
+   "rev": "acb60b64877e03f0184702506a006f157e37e044",
    "name": "mathlib",
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