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 m
from proveit.logic import Equals
from proveit.numbers import Mult, frac, i, pi, subtract, two
from proveit.physics.quantum.QPE import _phase, _two_pow_t

# build up the expression from sub-expressions
sub_expr1 = frac(Mult(two, pi, i, m), _two_pow_t)
expr = Equals(subtract(Mult(two, pi, i, _phase), sub_expr1), subtract(Mult(Mult(two, pi, i), _phase), sub_expr1))

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(2 \cdot \pi \cdot \mathsf{i} \cdot \varphi\right) - \frac{2 \cdot \pi \cdot \mathsf{i} \cdot m}{2^{t}}\right) = \left(\left(\left(2 \cdot \pi \cdot \mathsf{i}\right) \cdot \varphi\right) - \frac{2 \cdot \pi \cdot \mathsf{i} \cdot m}{2^{t}}\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, 10
6	Literal
7	ExprTuple	9, 10
8	Operation	operator: 23 operands: 11
9	Operation	operator: 23 operands: 12
10	Operation	operator: 13 operand: 17
11	ExprTuple	30, 27, 28, 16
12	ExprTuple	15, 16
13	Literal
14	ExprTuple	17
15	Operation	operator: 23 operands: 18
16	Literal
17	Operation	operator: 19 operands: 20
18	ExprTuple	30, 27, 28
19	Literal
20	ExprTuple	21, 22
21	Operation	operator: 23 operands: 24
22	Operation	operator: 25 operands: 26
23	Literal
24	ExprTuple	30, 27, 28, 29
25	Literal
26	ExprTuple	30, 31
27	Literal
28	Literal
29	Variable
30	Literal
31	Literal