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 ExprRange, ExprTuple, Variable, a, b, k, theta
from proveit.core_expr_types import Len
from proveit.numbers import Add, Exp, Mult, e, i, one, pi, two

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = ExprTuple(Len(operands = [Exp(e, Mult(two, pi, i, theta, k)), Exp(Add(a, b), k)]), Len(operands = [ExprRange(sub_expr1, sub_expr1, one, two)]))

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(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \theta \cdot k}, \left(a + b\right)^{k}\right)|, |\left(1, \ldots, 2\right)|\right)

stored_expr.style_options()

name	description	default	current value	related methods
wrap_positions	position(s) at which wrapping is to occur; 'n' is after the nth comma.	()	()	('with_wrapping_at',)
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	left	left	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1, 2
1	Operation	operator: 4 operands: 3
2	Operation	operator: 4 operands: 5
3	ExprTuple	6, 7
4	Literal
5	ExprTuple	8
6	Operation	operator: 10 operands: 9
7	Operation	operator: 10 operands: 11
8	ExprRange	lambda_map: 12 start_index: 13 end_index: 23
9	ExprTuple	14, 15
10	Literal
11	ExprTuple	16, 27
12	Lambda	parameter: 22 body: 22
13	Literal
14	Literal
15	Operation	operator: 18 operands: 19
16	Operation	operator: 20 operands: 21
17	ExprTuple	22
18	Literal
19	ExprTuple	23, 24, 25, 26, 27
20	Literal
21	ExprTuple	28, 29
22	Variable
23	Literal
24	Literal
25	Literal
26	Variable
27	Variable
28	Variable
29	Variable