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 Variable, m
from proveit.logic import Equals
from proveit.numbers import ModAbs, Mult, frac, one, subtract
from proveit.physics.quantum.QPE import _phase, _two_pow_t

# build up the expression from sub-expressions
expr = Equals(Mult(_two_pow_t, ModAbs(subtract(frac(m, _two_pow_t), _phase), one)), ModAbs(Variable("_a", latex_format = r"{_{-}a}"), _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(2^{t} \cdot \left|\frac{m}{2^{t}} - \varphi\right|_{\textup{mod}\thinspace 1}\right) = \left|{_{-}a}\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, 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 10 operands: 7
5	Literal
6	ExprTuple	23, 8
7	ExprTuple	9, 23
8	Operation	operator: 10 operands: 11
9	Variable
10	Literal
11	ExprTuple	12, 13
12	Operation	operator: 14 operands: 15
13	Literal
14	Literal
15	ExprTuple	16, 17
16	Operation	operator: 18 operands: 19
17	Operation	operator: 20 operand: 24
18	Literal
19	ExprTuple	22, 23
20	Literal
21	ExprTuple	24
22	Variable
23	Operation	operator: 25 operands: 26
24	Literal
25	Literal
26	ExprTuple	27, 28
27	Literal
28	Literal