Expression of type Conditional

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, IndexedVar, 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 = 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\{\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..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Conditional	value: 1 condition: 2
1	Operation	operator: 3 operands: 4
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7, 8
5	Literal
6	ExprTuple	9
7	Operation	operator: 31 operands: 10
8	Operation	operator: 16 operand: 14
9	ExprRange	lambda_map: 12 start_index: 42 end_index: 30
10	ExprTuple	34, 13, 36
11	ExprTuple	14
12	Lambda	parameter: 50 body: 15
13	Operation	operator: 16 operand: 21
14	Operation	operator: 24 operands: 18
15	Operation	operator: 19 operands: 20
16	Literal
17	ExprTuple	21
18	ExprTuple	22
19	Literal
20	ExprTuple	33, 23
21	Operation	operator: 24 operands: 25
22	ExprRange	lambda_map: 26 start_index: 42 end_index: 30
23	Literal
24	Literal
25	ExprTuple	27
26	Lambda	parameter: 45 body: 28
27	ExprRange	lambda_map: 29 start_index: 42 end_index: 30
28	Operation	operator: 31 operands: 32
29	Lambda	parameter: 50 body: 33
30	Variable
31	Literal
32	ExprTuple	34, 35, 36
33	IndexedVar	variable: 39 index: 50
34	ExprRange	lambda_map: 37 start_index: 42 end_index: 38
35	IndexedVar	variable: 39 index: 45
36	ExprRange	lambda_map: 41 start_index: 42 end_index: 43
37	Lambda	parameter: 50 body: 44
38	Variable
39	Variable
40	ExprTuple	45
41	Lambda	parameter: 50 body: 46
42	Literal
43	Variable
44	IndexedVar	variable: 47 index: 50
45	Variable
46	IndexedVar	variable: 48 index: 50
47	Variable
48	Variable
49	ExprTuple	50
50	Variable