Expression of type Conditional

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.linear_algebra import ScalarMult
from proveit.logic import CartExp, InSet
from proveit.numbers import Complex, Exp, Interval, Mult, e, i, one, pi, subtract, two, zero
from proveit.physics.quantum import NumKet
from proveit.physics.quantum.QPE import _phase, two_pow_t

# build up the expression from sub-expressions
expr = Conditional(InSet(ScalarMult(Exp(e, Mult(two, pi, i, _phase, k)), NumKet(k, t)), CartExp(Complex, two_pow_t)), InSet(k, Interval(zero, subtract(two_pow_t, one))))

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(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot k} \cdot \lvert k \rangle_{t}\right) \in \mathbb{C}^{2^{t}} \textrm{ if } k \in \{0~\ldotp \ldotp~2^{t} - 1\}\right..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Conditional	value: 1 condition: 2
1	Operation	operator: 4 operands: 3
2	Operation	operator: 4 operands: 5
3	ExprTuple	6, 7
4	Literal
5	ExprTuple	38, 8
6	Operation	operator: 9 operands: 10
7	Operation	operator: 11 operands: 12
8	Operation	operator: 13 operands: 14
9	Literal
10	ExprTuple	15, 16
11	Literal
12	ExprTuple	17, 27
13	Literal
14	ExprTuple	18, 19
15	Operation	operator: 31 operands: 20
16	Operation	operator: 21 operands: 22
17	Literal
18	Literal
19	Operation	operator: 23 operands: 24
20	ExprTuple	25, 26
21	Literal
22	ExprTuple	38, 40
23	Literal
24	ExprTuple	27, 28
25	Literal
26	Operation	operator: 29 operands: 30
27	Operation	operator: 31 operands: 32
28	Operation	operator: 33 operand: 41
29	Literal
30	ExprTuple	39, 35, 36, 37, 38
31	Literal
32	ExprTuple	39, 40
33	Literal
34	ExprTuple	41
35	Literal
36	Literal
37	Literal
38	Variable
39	Literal
40	Variable
41	Literal