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
expr = Equals(subtract(Mult(two, pi, i, _phase), frac(Mult(two, pi, i, m), _two_pow_t)), Mult(Mult(two, pi, i), subtract(_phase, frac(m, _two_pow_t))))

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(2 \cdot \pi \cdot \mathsf{i}\right) \cdot \left(\varphi - \frac{m}{2^{t}}\right)\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: 14 operands: 5
4	Operation	operator: 24 operands: 6
5	ExprTuple	7, 8
6	ExprTuple	9, 10
7	Operation	operator: 24 operands: 11
8	Operation	operator: 20 operand: 16
9	Operation	operator: 24 operands: 13
10	Operation	operator: 14 operands: 15
11	ExprTuple	34, 28, 29, 17
12	ExprTuple	16
13	ExprTuple	34, 28, 29
14	Literal
15	ExprTuple	17, 18
16	Operation	operator: 26 operands: 19
17	Literal
18	Operation	operator: 20 operand: 23
19	ExprTuple	22, 31
20	Literal
21	ExprTuple	23
22	Operation	operator: 24 operands: 25
23	Operation	operator: 26 operands: 27
24	Literal
25	ExprTuple	34, 28, 29, 30
26	Literal
27	ExprTuple	30, 31
28	Literal
29	Literal
30	Variable
31	Operation	operator: 32 operands: 33
32	Literal
33	ExprTuple	34, 35
34	Literal
35	Literal