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refactor(*): assume ≠0 instead of 0 < _ #17612

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fee1907
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urkud Nov 3, 2022
16ddb3a
chore(data/polynomial/degree): golf a proof
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Update src/data/polynomial/degree/definitions.lean
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Merge branch 'master' into YK-nat-prime-iff
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Update src/data/nat/prime.lean
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Merge branch 'master' into YK-nat-pos
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Merge branch 'YK-nat-prime-iff' into YK-nat-pos
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Merge branch 'master' into YK-nat-pos
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Merge remote-tracking branch 'origin/YK-nat-prime-iff' into YK-nat-pos
urkud Nov 9, 2022
062f5e1
Fix `norm_num`
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Merge branch 'master' into YK-nat-pos
urkud Nov 10, 2022
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urkud Nov 12, 2022
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Merge branch 'master' into YK-nat-pos
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Fix, golf
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urkud Nov 13, 2022
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c4b2329
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f081081
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Merge branch 'YK-cyclotomic' into YK-nat-pos
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Merge branch 'master' into YK-prim-roots-golf
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Merge branch 'YK-prim-roots-golf' into YK-nat-pos
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urkud Nov 17, 2022
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urkud Nov 18, 2022
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Fix, golf
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Merge branch 'master' into YK-nat-pos
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Merge branch 'master' into YK-nat-pos
urkud Nov 20, 2022
9d93764
feat(ring_theory/integral_domain): generalize `card_fiber_eq_of_mem_r…
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Golf
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Merge branch 'YK-card-fiber-eq' into YK-nat-pos
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urkud Nov 24, 2022
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Merge branch 'master' into YK-nat-pos
urkud Dec 3, 2022
0697336
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urkud Dec 3, 2022
23acf65
Fix
urkud Dec 3, 2022
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urkud Dec 4, 2022
c60c141
Merge branch 'master' into YK-nat-pos
urkud Dec 4, 2022
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urkud Dec 4, 2022
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46bc072
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urkud Dec 6, 2022
3b30776
Merge branch 'master' into YK-nat-pos
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2e5140e
Long line
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Merge branch 'master' into YK-nat-pos
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Merge branch 'master' into YK-nat-pos
urkud Dec 9, 2022
c03f8d8
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urkud Dec 9, 2022
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urkud Dec 10, 2022
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urkud Dec 10, 2022
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urkud Dec 10, 2022
d27ca25
chore(number_theory/padics/padic_val): golf
urkud Dec 10, 2022
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urkud Dec 10, 2022
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urkud Dec 11, 2022
ee78b0a
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urkud Dec 11, 2022
ba975fe
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urkud Dec 11, 2022
2259027
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urkud Dec 12, 2022
eb06f18
Merge branch 'master' into YK-nat-pos
urkud Dec 12, 2022
5a22e4b
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urkud Dec 13, 2022
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urkud Dec 13, 2022
015b564
Merge branch 'master' into YK-nat-pos
urkud Dec 21, 2022
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Merge branch 'master' into YK-nat-pos
urkud Dec 26, 2022
aaa60b7
Fix
urkud Dec 29, 2022
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Cherry-pick
urkud Dec 29, 2022
cb13f33
Fix
urkud Dec 29, 2022
9ab7e8a
Fix
urkud Dec 29, 2022
7135a58
Golf, use `≠ 0`
urkud Dec 29, 2022
d57fa3b
Fix
urkud Dec 29, 2022
94f97ed
Merge branch 'YK-cycl-eval' into YK-nat-pos
urkud Dec 29, 2022
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...
urkud Dec 29, 2022
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Merge branch 'YK-cycl-eval' into YK-nat-pos
urkud Dec 29, 2022
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urkud Dec 29, 2022
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Golf, fix
urkud Dec 30, 2022
7335963
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urkud Dec 30, 2022
e15cf09
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urkud Dec 30, 2022
edf7bbf
Merge branch 'master' into YK-nat-pos
urkud Dec 30, 2022
aae7e91
Fix, golf
urkud Dec 30, 2022
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urkud Dec 30, 2022
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Merge branch 'master' into YK-nat-pos
urkud Jan 7, 2023
6532224
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urkud Jan 7, 2023
9de5595
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urkud Jan 7, 2023
25e44db
Fix test
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Merge branch 'master' into YK-nat-pos
urkud Jan 11, 2023
c4ee919
Fix
urkud Jan 11, 2023
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Merge branch 'master' into YK-nat-pos
urkud Jan 11, 2023
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Merge branch 'master' into YK-nat-pos
urkud Jan 14, 2023
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Snapshot
urkud Jan 14, 2023
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Merge branch 'master' into YK-cons-divisors
urkud Jan 14, 2023
a7f4688
Swap LHS and RHS
urkud Jan 15, 2023
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Merge branch 'master' into YK-cons-divisors
urkud Jan 16, 2023
5eb10e6
Merge branch 'YK-cons-divisors' into YK-nat-pos
urkud Jan 16, 2023
5358341
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Merge branch 'master' into YK-nat-pos
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Fix
urkud committed Dec 9, 2022

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commit d2d3dc2501c743d8f3388cb6594b738c1fb63938
5 changes: 3 additions & 2 deletions src/data/nat/choose/multinomial.lean
Original file line number Diff line number Diff line change
@@ -41,8 +41,9 @@ Defined as `(∑ i in s, f i)! / ∏ i in s, (f i)!`.
-/
def multinomial : ℕ := (∑ i in s, f i)! / ∏ i in s, (f i)!

lemma multinomial_pos : 0 < multinomial s f := nat.div_pos
(le_of_dvd (factorial_pos _) (prod_factorial_dvd_factorial_sum s f)) (prod_factorial_pos s f)
lemma multinomial_pos : 0 < multinomial s f :=
nat.div_pos (le_of_dvd (factorial_pos _) (prod_factorial_dvd_factorial_sum s f))
(prod_factorial_pos s f).ne'

lemma multinomial_spec : (∏ i in s, (f i)!) * multinomial s f = (∑ i in s, f i)! :=
nat.mul_div_cancel' (prod_factorial_dvd_factorial_sum s f)