Expression of type ExprTuple

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, ExprTuple, IndexedVar, Lambda, 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 = ExprTuple(Lambda([x_1_to_n], 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}, x_{2}, \ldots, x_{n}\right) \mapsto \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..\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: 19 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: 29 operand: 15
10	Operation	operator: 18 operands: 13
11	ExprRange	lambda_map: 14 start_index: 27 end_index: 28
12	ExprTuple	15
13	ExprTuple	16
14	Lambda	parameter: 34 body: 17
15	Operation	operator: 18 operands: 19
16	ExprRange	lambda_map: 20 start_index: 27 end_index: 28
17	Operation	operator: 21 operands: 22
18	Literal
19	ExprTuple	23
20	Lambda	parameter: 34 body: 24
21	Literal
22	ExprTuple	31, 25
23	ExprRange	lambda_map: 26 start_index: 27 end_index: 28
24	Operation	operator: 29 operand: 31
25	Literal
26	Lambda	parameter: 34 body: 31
27	Literal
28	Variable
29	Literal
30	ExprTuple	31
31	IndexedVar	variable: 32 index: 34
32	Variable
33	ExprTuple	34
34	Variable