Expression of type Conditional

from the theory of proveit.numbers.absolute_value

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, n, x
from proveit.core_expr_types import x_1_to_n
from proveit.logic import And, Equals, InSet
from proveit.numbers import Abs, Complex, Mult, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = IndexedVar(x, sub_expr1)
expr = Conditional(Equals(Abs(Mult(x_1_to_n)), Mult(ExprRange(sub_expr1, Abs(sub_expr2), one, n))), And(ExprRange(sub_expr1, InSet(sub_expr2, Complex), one, n)))

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|x_{1} \cdot  x_{2} \cdot  \ldots \cdot  x_{n}\right| = \left(\left|x_{1}\right| \cdot  \left|x_{2}\right| \cdot  \ldots \cdot  \left|x_{n}\right|\right) \textrm{ if } \left(x_{1} \in \mathbb{C}\right) \land  \left(x_{2} \in \mathbb{C}\right) \land  \ldots \land  \left(x_{n} \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: 27 operand: 13
8	Operation	operator: 16 operands: 11
9	ExprRange	lambda_map: 12 start_index: 25 end_index: 26
10	ExprTuple	13
11	ExprTuple	14
12	Lambda	parameter: 32 body: 15
13	Operation	operator: 16 operands: 17
14	ExprRange	lambda_map: 18 start_index: 25 end_index: 26
15	Operation	operator: 19 operands: 20
16	Literal
17	ExprTuple	21
18	Lambda	parameter: 32 body: 22
19	Literal
20	ExprTuple	29, 23
21	ExprRange	lambda_map: 24 start_index: 25 end_index: 26
22	Operation	operator: 27 operand: 29
23	Literal
24	Lambda	parameter: 32 body: 29
25	Literal
26	Variable
27	Literal
28	ExprTuple	29
29	IndexedVar	variable: 30 index: 32
30	Variable
31	ExprTuple	32
32	Variable