Expression of type Equals

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, Variable, b, delta, k, theta
from proveit.core_expr_types import Len
from proveit.logic import Equals
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 = Equals(Len(operands = [Exp(e, Mult(Add(Mult(two, pi, i, delta), Mult(two, pi, i, theta)), k)), Exp(e, Mult(two, pi, i, b))]), 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(\mathsf{e}^{\left(\left(2 \cdot \pi \cdot \mathsf{i} \cdot \delta\right) + \left(2 \cdot \pi \cdot \mathsf{i} \cdot \theta\right)\right) \cdot k}, \mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot b}\right)| = |\left(1, \ldots, 2\right)|

stored_expr.style_options()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix
wrap_positions	position(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.	()	()	('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)
direction	Direction of the relation (normal or reversed)	normal	normal	('with_direction_reversed', 'is_reversed')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operands: 2
1	Literal
2	ExprTuple	3, 4
3	Operation	operator: 6 operands: 5
4	Operation	operator: 6 operands: 7
5	ExprTuple	8, 9
6	Literal
7	ExprTuple	10
8	Operation	operator: 12 operands: 11
9	Operation	operator: 12 operands: 13
10	ExprRange	lambda_map: 14 start_index: 15 end_index: 34
11	ExprTuple	17, 16
12	Literal
13	ExprTuple	17, 18
14	Lambda	parameter: 22 body: 22
15	Literal
16	Operation	operator: 31 operands: 20
17	Literal
18	Operation	operator: 31 operands: 21
19	ExprTuple	22
20	ExprTuple	23, 24
21	ExprTuple	34, 35, 36, 25
22	Variable
23	Operation	operator: 26 operands: 27
24	Variable
25	Variable
26	Literal
27	ExprTuple	28, 29
28	Operation	operator: 31 operands: 30
29	Operation	operator: 31 operands: 32
30	ExprTuple	34, 35, 36, 33
31	Literal
32	ExprTuple	34, 35, 36, 37
33	Variable
34	Literal
35	Literal
36	Literal
37	Variable