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 Add, Floor, ModAbs, Mult, Neg, subtract
from proveit.physics.quantum.QPE import _phase, _two_pow_t

# build up the expression from sub-expressions
sub_expr1 = Mult(_two_pow_t, _phase)
sub_expr2 = ModAbs(subtract(m, sub_expr1), _two_pow_t)
sub_expr3 = ModAbs(subtract(m, Floor(sub_expr1)), _two_pow_t)
expr = Equals(Add(sub_expr3, sub_expr2, Neg(sub_expr3)), sub_expr2)

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|m - \left\lfloor 2^{t} \cdot \varphi\right\rfloor\right|_{\textup{mod}\thinspace 2^{t}} + \left|m - \left(2^{t} \cdot \varphi\right)\right|_{\textup{mod}\thinspace 2^{t}} - \left|m - \left\lfloor 2^{t} \cdot \varphi\right\rfloor\right|_{\textup{mod}\thinspace 2^{t}}\right) = \left|m - \left(2^{t} \cdot \varphi\right)\right|_{\textup{mod}\thinspace 2^{t}}

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