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Definition df-lmat 30218
Description: Define a function converting words of words into matrices. (Contributed by Thierry Arnoux, 28-Aug-2020.)
Assertion
Ref Expression
df-lmat litMat = (𝑚 ∈ V ↦ (𝑖 ∈ (1...(♯‘𝑚)), 𝑗 ∈ (1...(♯‘(𝑚‘0))) ↦ ((𝑚‘(𝑖 − 1))‘(𝑗 − 1))))
Distinct variable group:   𝑖,𝑗,𝑚

Detailed syntax breakdown of Definition df-lmat
StepHypRef Expression
1 clmat 30217 . 2 class litMat
2 vm . . 3 setvar 𝑚
3 cvv 3351 . . 3 class V
4 vi . . . 4 setvar 𝑖
5 vj . . . 4 setvar 𝑗
6 c1 10143 . . . . 5 class 1
72cv 1630 . . . . . 6 class 𝑚
8 chash 13321 . . . . . 6 class
97, 8cfv 6030 . . . . 5 class (♯‘𝑚)
10 cfz 12533 . . . . 5 class ...
116, 9, 10co 6796 . . . 4 class (1...(♯‘𝑚))
12 cc0 10142 . . . . . . 7 class 0
1312, 7cfv 6030 . . . . . 6 class (𝑚‘0)
1413, 8cfv 6030 . . . . 5 class (♯‘(𝑚‘0))
156, 14, 10co 6796 . . . 4 class (1...(♯‘(𝑚‘0)))
165cv 1630 . . . . . 6 class 𝑗
17 cmin 10472 . . . . . 6 class
1816, 6, 17co 6796 . . . . 5 class (𝑗 − 1)
194cv 1630 . . . . . . 7 class 𝑖
2019, 6, 17co 6796 . . . . . 6 class (𝑖 − 1)
2120, 7cfv 6030 . . . . 5 class (𝑚‘(𝑖 − 1))
2218, 21cfv 6030 . . . 4 class ((𝑚‘(𝑖 − 1))‘(𝑗 − 1))
234, 5, 11, 15, 22cmpt2 6798 . . 3 class (𝑖 ∈ (1...(♯‘𝑚)), 𝑗 ∈ (1...(♯‘(𝑚‘0))) ↦ ((𝑚‘(𝑖 − 1))‘(𝑗 − 1)))
242, 3, 23cmpt 4864 . 2 class (𝑚 ∈ V ↦ (𝑖 ∈ (1...(♯‘𝑚)), 𝑗 ∈ (1...(♯‘(𝑚‘0))) ↦ ((𝑚‘(𝑖 − 1))‘(𝑗 − 1))))
251, 24wceq 1631 1 wff litMat = (𝑚 ∈ V ↦ (𝑖 ∈ (1...(♯‘𝑚)), 𝑗 ∈ (1...(♯‘(𝑚‘0))) ↦ ((𝑚‘(𝑖 − 1))‘(𝑗 − 1))))
Colors of variables: wff setvar class
This definition is referenced by:  lmatval  30219
  Copyright terms: Public domain W3C validator