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.logic import Equals
from proveit.numbers import Add, Exp, Mult, Neg, frac, one, subtract, two
from proveit.physics.quantum.QPE import _t, _two_pow_t

# build up the expression from sub-expressions
sub_expr1 = frac(one, two)
sub_expr2 = Mult(sub_expr1, frac(one, _two_pow_t))
sub_expr3 = subtract(Neg(sub_expr1), sub_expr2)
expr = Equals(Add(sub_expr2, sub_expr3), Add(Mult(sub_expr1, Exp(two, Neg(_t))), sub_expr3))

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(\frac{1}{2} \cdot \frac{1}{2^{t}}\right) + \left(-\frac{1}{2} - \left(\frac{1}{2} \cdot \frac{1}{2^{t}}\right)\right)\right) = \left(\left(\frac{1}{2} \cdot 2^{-t}\right) + \left(-\frac{1}{2} - \left(\frac{1}{2} \cdot \frac{1}{2^{t}}\right)\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: 10 operands: 5
4	Operation	operator: 10 operands: 6
5	ExprTuple	19, 8
6	ExprTuple	7, 8
7	Operation	operator: 22 operands: 9
8	Operation	operator: 10 operands: 11
9	ExprTuple	24, 12
10	Literal
11	ExprTuple	13, 14
12	Operation	operator: 31 operands: 15
13	Operation	operator: 20 operand: 24
14	Operation	operator: 20 operand: 19
15	ExprTuple	33, 18
16	ExprTuple	24
17	ExprTuple	19
18	Operation	operator: 20 operand: 34
19	Operation	operator: 22 operands: 23
20	Literal
21	ExprTuple	34
22	Literal
23	ExprTuple	24, 25
24	Operation	operator: 27 operands: 26
25	Operation	operator: 27 operands: 28
26	ExprTuple	29, 33
27	Literal
28	ExprTuple	29, 30
29	Literal
30	Operation	operator: 31 operands: 32
31	Literal
32	ExprTuple	33, 34
33	Literal
34	Literal