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 Conditional, k, t
from proveit.logic import Equals, InSet
from proveit.numbers import Add, Interval, one, subtract, zero
from proveit.physics.quantum import NumKet
from proveit.physics.quantum.QPE import two_pow_t

# build up the expression from sub-expressions
sub_expr1 = NumKet(k, Add(t, one))
expr = Equals(Conditional(sub_expr1, InSet(k, Interval(zero, subtract(two_pow_t, one)))), sub_expr1)

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\{\lvert k \rangle_{t + 1} \textrm{ if } k \in \{0~\ldotp \ldotp~2^{t} - 1\}\right.. = \lvert k \rangle_{t + 1}

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