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.linear_algebra import Norm
from proveit.logic import Equals
from proveit.numbers import Add, Exp, sqrt, two
from proveit.physics.quantum import ket0, ket1

# build up the expression from sub-expressions
expr = Equals(sqrt(Add(Exp(Norm(ket0), two), Exp(Norm(ket1), two))), sqrt(two))

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())

\sqrt{\left(\left \|\lvert 0 \rangle\right \|^{2} + \left \|\lvert 1 \rangle\right \|^{2}\right)} = \sqrt{2}

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