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, Neg, e, i, pi, subtract, two
from proveit.physics.quantum.QPE import _delta_b_floor, _t

# build up the expression from sub-expressions
sub_expr1 = subtract(_delta_b_floor, Mult(l, Exp(two, Neg(_t))))
expr = Equals(Exp(e, Mult(i, Mult(two, pi, sub_expr1))), Exp(e, Mult(two, pi, sub_expr1, i)))

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())

\mathsf{e}^{\mathsf{i} \cdot \left(2 \cdot \pi \cdot \left(\delta_{b_{\textit{f}}} - \left(l \cdot 2^{-t}\right)\right)\right)} = \mathsf{e}^{2 \cdot \pi \cdot \left(\delta_{b_{\textit{f}}} - \left(l \cdot 2^{-t}\right)\right) \cdot \mathsf{i}}

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: 30 operands: 5
4	Operation	operator: 30 operands: 6
5	ExprTuple	8, 7
6	ExprTuple	8, 9
7	Operation	operator: 26 operands: 10
8	Literal
9	Operation	operator: 26 operands: 11
10	ExprTuple	13, 12
11	ExprTuple	32, 15, 16, 13
12	Operation	operator: 26 operands: 14
13	Literal
14	ExprTuple	32, 15, 16
15	Literal
16	Operation	operator: 17 operands: 18
17	Literal
18	ExprTuple	19, 20
19	Operation	operator: 21 operand: 24
20	Operation	operator: 34 operand: 25
21	Literal
22	ExprTuple	24
23	ExprTuple	25
24	Literal
25	Operation	operator: 26 operands: 27
26	Literal
27	ExprTuple	28, 29
28	Variable
29	Operation	operator: 30 operands: 31
30	Literal
31	ExprTuple	32, 33
32	Literal
33	Operation	operator: 34 operand: 36
34	Literal
35	ExprTuple	36
36	Literal