Expression of type ExprTuple

from the theory of proveit.numbers.multiplication

import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import Conditional, ExprRange, ExprTuple, IndexedVar, Lambda, Variable, b, i, j, k
from proveit.core_expr_types import a_1_to_i, b_1_to_j, c_1_to_k
from proveit.logic import And, Equals, Forall, InSet
from proveit.numbers import Abs, Add, Complex, Mult, Natural, RealNonNeg, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_b", latex_format = r"{_{-}b}")
expr = ExprTuple(Lambda([i, j, k], Conditional(Forall(instance_param_or_params = [a_1_to_i, c_1_to_k], instance_expr = Forall(instance_param_or_params = [b_1_to_j], instance_expr = Equals(Mult(a_1_to_i, Abs(Add(b_1_to_j)), c_1_to_k), Abs(Add(ExprRange(sub_expr1, Mult(a_1_to_i, IndexedVar(b, sub_expr1), c_1_to_k), one, j)))).with_wrapping_at(2), domain = Complex).with_wrapping(), domain = RealNonNeg).with_wrapping(), And(InSet(i, Natural), InSet(j, Natural), InSet(k, Natural)))))

expr:

# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")

Passed sanity check: expr matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\left(\left(i, j, k\right) \mapsto \left\{\begin{array}{l}\forall_{a_{1}, a_{2}, \ldots, a_{i}, c_{1}, c_{2}, \ldots, c_{k} \in \mathbb{R}^{\ge 0}}~\\
\left[\begin{array}{l}\forall_{b_{1}, b_{2}, \ldots, b_{j} \in \mathbb{C}}~\\
\left(\begin{array}{c} \begin{array}{l} \left(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{i} \cdot \left|b_{1} +  b_{2} +  \ldots +  b_{j}\right|\cdot c_{1} \cdot  c_{2} \cdot  \ldots \cdot  c_{k}\right) =  \\ \left|\left(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{i} \cdot b_{1}\cdot c_{1} \cdot  c_{2} \cdot  \ldots \cdot  c_{k}\right) +  \left(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{i} \cdot b_{2}\cdot c_{1} \cdot  c_{2} \cdot  \ldots \cdot  c_{k}\right) +  \ldots +  \left(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{i} \cdot b_{j}\cdot c_{1} \cdot  c_{2} \cdot  \ldots \cdot  c_{k}\right)\right| \end{array} \end{array}\right)\end{array}\right]\end{array} \textrm{ if } i \in \mathbb{N} ,  j \in \mathbb{N} ,  k \in \mathbb{N}\right..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameters: 2 body: 3
2	ExprTuple	71, 63, 76
3	Conditional	value: 4 condition: 5
4	Operation	operator: 20 operand: 8
5	Operation	operator: 35 operands: 7
6	ExprTuple	8
7	ExprTuple	9, 10, 11
8	Lambda	parameters: 12 body: 13
9	Operation	operator: 52 operands: 14
10	Operation	operator: 52 operands: 15
11	Operation	operator: 52 operands: 16
12	ExprTuple	67, 69
13	Conditional	value: 17 condition: 18
14	ExprTuple	71, 19
15	ExprTuple	63, 19
16	ExprTuple	76, 19
17	Operation	operator: 20 operand: 23
18	Operation	operator: 35 operands: 22
19	Literal
20	Literal
21	ExprTuple	23
22	ExprTuple	24, 25
23	Lambda	parameters: 58 body: 26
24	ExprRange	lambda_map: 27 start_index: 75 end_index: 71
25	ExprRange	lambda_map: 28 start_index: 75 end_index: 76
26	Conditional	value: 29 condition: 30
27	Lambda	parameter: 83 body: 31
28	Lambda	parameter: 83 body: 32
29	Operation	operator: 33 operands: 34
30	Operation	operator: 35 operands: 36
31	Operation	operator: 52 operands: 37
32	Operation	operator: 52 operands: 38
33	Literal
34	ExprTuple	39, 40
35	Literal
36	ExprTuple	41
37	ExprTuple	77, 42
38	ExprTuple	79, 42
39	Operation	operator: 64 operands: 43
40	Operation	operator: 49 operand: 47
41	ExprRange	lambda_map: 45 start_index: 75 end_index: 63
42	Literal
43	ExprTuple	67, 46, 69
44	ExprTuple	47
45	Lambda	parameter: 83 body: 48
46	Operation	operator: 49 operand: 54
47	Operation	operator: 57 operands: 51
48	Operation	operator: 52 operands: 53
49	Literal
50	ExprTuple	54
51	ExprTuple	55
52	Literal
53	ExprTuple	66, 56
54	Operation	operator: 57 operands: 58
55	ExprRange	lambda_map: 59 start_index: 75 end_index: 63
56	Literal
57	Literal
58	ExprTuple	60
59	Lambda	parameter: 78 body: 61
60	ExprRange	lambda_map: 62 start_index: 75 end_index: 63
61	Operation	operator: 64 operands: 65
62	Lambda	parameter: 83 body: 66
63	Variable
64	Literal
65	ExprTuple	67, 68, 69
66	IndexedVar	variable: 72 index: 83
67	ExprRange	lambda_map: 70 start_index: 75 end_index: 71
68	IndexedVar	variable: 72 index: 78
69	ExprRange	lambda_map: 74 start_index: 75 end_index: 76
70	Lambda	parameter: 83 body: 77
71	Variable
72	Variable
73	ExprTuple	78
74	Lambda	parameter: 83 body: 79
75	Literal
76	Variable
77	IndexedVar	variable: 80 index: 83
78	Variable
79	IndexedVar	variable: 81 index: 83
80	Variable
81	Variable
82	ExprTuple	83
83	Variable