Expression of type Equals

from the theory of proveit.physics.quantum.QPE

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 k
from proveit.logic import Equals
from proveit.numbers import Exp, Mult, Neg, e, frac, i, one, pi, two
from proveit.physics.quantum.QPE import _phase, _two_pow_t

# build up the expression from sub-expressions
expr = Equals(Mult(Exp(e, Neg(frac(Mult(two, pi, i, k, Mult(_two_pow_t, _phase)), _two_pow_t))), Exp(e, Mult(two, pi, i, _phase, k))), one)

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}^{-\frac{2 \cdot \pi \cdot \mathsf{i} \cdot k \cdot \left(2^{t} \cdot \varphi\right)}{2^{t}}} \cdot \mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot k}\right) = 1

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: 25 operands: 5
4	Literal
5	ExprTuple	6, 7
6	Operation	operator: 29 operands: 8
7	Operation	operator: 29 operands: 9
8	ExprTuple	11, 10
9	ExprTuple	11, 12
10	Operation	operator: 13 operand: 16
11	Literal
12	Operation	operator: 25 operands: 15
13	Literal
14	ExprTuple	16
15	ExprTuple	31, 21, 22, 28, 23
16	Operation	operator: 17 operands: 18
17	Literal
18	ExprTuple	19, 27
19	Operation	operator: 25 operands: 20
20	ExprTuple	31, 21, 22, 23, 24
21	Literal
22	Literal
23	Variable
24	Operation	operator: 25 operands: 26
25	Literal
26	ExprTuple	27, 28
27	Operation	operator: 29 operands: 30
28	Literal
29	Literal
30	ExprTuple	31, 32
31	Literal
32	Literal