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, j
from proveit.core_expr_types import a_1_to_i, b_1_to_j, c_1_to_k
from proveit.logic import And, Equals, InSet
from proveit.numbers import Abs, Add, Complex, Mult, 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([b_1_to_j], Conditional(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), And(ExprRange(sub_expr2, InSet(IndexedVar(b, sub_expr2), Complex), one, j)))))

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(b_{1}, b_{2}, \ldots, b_{j}\right) \mapsto \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} \textrm{ if } \left(b_{1} \in \mathbb{C}\right) \land  \left(b_{2} \in \mathbb{C}\right) \land  \ldots \land  \left(b_{j} \in \mathbb{C}\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: 27 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9, 10
7	Literal
8	ExprTuple	11
9	Operation	operator: 33 operands: 12
10	Operation	operator: 18 operand: 16
11	ExprRange	lambda_map: 14 start_index: 44 end_index: 32
12	ExprTuple	36, 15, 38
13	ExprTuple	16
14	Lambda	parameter: 52 body: 17
15	Operation	operator: 18 operand: 23
16	Operation	operator: 26 operands: 20
17	Operation	operator: 21 operands: 22
18	Literal
19	ExprTuple	23
20	ExprTuple	24
21	Literal
22	ExprTuple	35, 25
23	Operation	operator: 26 operands: 27
24	ExprRange	lambda_map: 28 start_index: 44 end_index: 32
25	Literal
26	Literal
27	ExprTuple	29
28	Lambda	parameter: 47 body: 30
29	ExprRange	lambda_map: 31 start_index: 44 end_index: 32
30	Operation	operator: 33 operands: 34
31	Lambda	parameter: 52 body: 35
32	Variable
33	Literal
34	ExprTuple	36, 37, 38
35	IndexedVar	variable: 41 index: 52
36	ExprRange	lambda_map: 39 start_index: 44 end_index: 40
37	IndexedVar	variable: 41 index: 47
38	ExprRange	lambda_map: 43 start_index: 44 end_index: 45
39	Lambda	parameter: 52 body: 46
40	Variable
41	Variable
42	ExprTuple	47
43	Lambda	parameter: 52 body: 48
44	Literal
45	Variable
46	IndexedVar	variable: 49 index: 52
47	Variable
48	IndexedVar	variable: 50 index: 52
49	Variable
50	Variable
51	ExprTuple	52
52	Variable