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, a, b, c, 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, RealNonNeg, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_b", latex_format = r"{_{-}b}")
sub_expr2 = Variable("_a", latex_format = r"{_{-}a}")
expr = ExprTuple(Lambda([a_1_to_i, c_1_to_k], Conditional(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(), And(ExprRange(sub_expr2, InSet(IndexedVar(a, sub_expr2), RealNonNeg), one, i), ExprRange(sub_expr2, InSet(IndexedVar(c, sub_expr2), RealNonNeg), one, k)))))

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(a_{1}, a_{2}, \ldots, a_{i}, c_{1}, c_{2}, \ldots, c_{k}\right) \mapsto \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} \textrm{ if } \left(a_{1} \in \mathbb{R}^{\ge 0}\right) ,  \left(a_{2} \in \mathbb{R}^{\ge 0}\right) ,  \ldots ,  \left(a_{i} \in \mathbb{R}^{\ge 0}\right), \left(c_{1} \in \mathbb{R}^{\ge 0}\right) ,  \left(c_{2} \in \mathbb{R}^{\ge 0}\right) ,  \ldots ,  \left(c_{k} \in \mathbb{R}^{\ge 0}\right)\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	53, 55
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 9
5	Operation	operator: 21 operands: 8
6	Literal
7	ExprTuple	9
8	ExprTuple	10, 11
9	Lambda	parameters: 44 body: 12
10	ExprRange	lambda_map: 13 start_index: 61 end_index: 57
11	ExprRange	lambda_map: 14 start_index: 61 end_index: 62
12	Conditional	value: 15 condition: 16
13	Lambda	parameter: 69 body: 17
14	Lambda	parameter: 69 body: 18
15	Operation	operator: 19 operands: 20
16	Operation	operator: 21 operands: 22
17	Operation	operator: 38 operands: 23
18	Operation	operator: 38 operands: 24
19	Literal
20	ExprTuple	25, 26
21	Literal
22	ExprTuple	27
23	ExprTuple	63, 28
24	ExprTuple	65, 28
25	Operation	operator: 50 operands: 29
26	Operation	operator: 35 operand: 33
27	ExprRange	lambda_map: 31 start_index: 61 end_index: 49
28	Literal
29	ExprTuple	53, 32, 55
30	ExprTuple	33
31	Lambda	parameter: 69 body: 34
32	Operation	operator: 35 operand: 40
33	Operation	operator: 43 operands: 37
34	Operation	operator: 38 operands: 39
35	Literal
36	ExprTuple	40
37	ExprTuple	41
38	Literal
39	ExprTuple	52, 42
40	Operation	operator: 43 operands: 44
41	ExprRange	lambda_map: 45 start_index: 61 end_index: 49
42	Literal
43	Literal
44	ExprTuple	46
45	Lambda	parameter: 64 body: 47
46	ExprRange	lambda_map: 48 start_index: 61 end_index: 49
47	Operation	operator: 50 operands: 51
48	Lambda	parameter: 69 body: 52
49	Variable
50	Literal
51	ExprTuple	53, 54, 55
52	IndexedVar	variable: 58 index: 69
53	ExprRange	lambda_map: 56 start_index: 61 end_index: 57
54	IndexedVar	variable: 58 index: 64
55	ExprRange	lambda_map: 60 start_index: 61 end_index: 62
56	Lambda	parameter: 69 body: 63
57	Variable
58	Variable
59	ExprTuple	64
60	Lambda	parameter: 69 body: 65
61	Literal
62	Variable
63	IndexedVar	variable: 66 index: 69
64	Variable
65	IndexedVar	variable: 67 index: 69
66	Variable
67	Variable
68	ExprTuple	69
69	Variable