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 l
from proveit.logic import Equals
from proveit.numbers import Exp, Mult, e, i, one, pi, subtract, two
from proveit.physics.quantum.QPE import _delta_b_floor, _two_pow_t

# build up the expression from sub-expressions
expr = Equals(subtract(one, Exp(e, Mult(two, pi, i, subtract(Mult(_delta_b_floor, _two_pow_t), l)))), subtract(one, Exp(e, Mult(two, pi, i, subtract(Mult(_two_pow_t, _delta_b_floor), l)))))

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(1 - \mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \left(\left(\delta_{b_{\textit{f}}} \cdot 2^{t}\right) - l\right)}\right) = \left(1 - \mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \left(\left(2^{t} \cdot \delta_{b_{\textit{f}}}\right) - l\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: 26 operands: 5
4	Operation	operator: 26 operands: 6
5	ExprTuple	8, 7
6	ExprTuple	8, 9
7	Operation	operator: 34 operand: 12
8	Literal
9	Operation	operator: 34 operand: 13
10	ExprTuple	12
11	ExprTuple	13
12	Operation	operator: 39 operands: 14
13	Operation	operator: 39 operands: 15
14	ExprTuple	17, 16
15	ExprTuple	17, 18
16	Operation	operator: 32 operands: 19
17	Literal
18	Operation	operator: 32 operands: 20
19	ExprTuple	43, 22, 23, 21
20	ExprTuple	43, 22, 23, 24
21	Operation	operator: 26 operands: 25
22	Literal
23	Literal
24	Operation	operator: 26 operands: 27
25	ExprTuple	28, 30
26	Literal
27	ExprTuple	29, 30
28	Operation	operator: 32 operands: 31
29	Operation	operator: 32 operands: 33
30	Operation	operator: 34 operand: 38
31	ExprTuple	37, 36
32	Literal
33	ExprTuple	36, 37
34	Literal
35	ExprTuple	38
36	Operation	operator: 39 operands: 40
37	Operation	operator: 41 operand: 45
38	Variable
39	Literal
40	ExprTuple	43, 44
41	Literal
42	ExprTuple	45
43	Literal
44	Literal
45	Literal