Expression of type ExprTuple

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, ExprTuple, Lambda, k, t
from proveit.linear_algebra import ScalarMult, TensorProd
from proveit.logic import InSet
from proveit.numbers import Exp, Interval, Mult, e, i, one, pi, subtract, two, zero
from proveit.physics.quantum import NumKet, ket1
from proveit.physics.quantum.QPE import _phase, two_pow_t

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(k, Conditional(ScalarMult(Exp(e, Mult(two, pi, i, _phase, k)), TensorProd(ket1, NumKet(k, 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(k \mapsto \left\{\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot k} \cdot \left(\lvert 1 \rangle {\otimes} \lvert k \rangle_{t}\right) \textrm{ if } k \in \{0~\ldotp \ldotp~2^{t} - 1\}\right..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameter: 34 body: 3
2	ExprTuple	34
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operands: 7
5	Operation	operator: 8 operands: 9
6	Literal
7	ExprTuple	10, 11
8	Literal
9	ExprTuple	34, 12
10	Operation	operator: 37 operands: 13
11	Operation	operator: 14 operands: 15
12	Operation	operator: 16 operands: 17
13	ExprTuple	18, 19
14	Literal
15	ExprTuple	20, 21
16	Literal
17	ExprTuple	22, 23
18	Literal
19	Operation	operator: 24 operands: 25
20	Operation	operator: 26 operand: 43
21	Operation	operator: 27 operands: 28
22	Literal
23	Operation	operator: 29 operands: 30
24	Literal
25	ExprTuple	41, 31, 32, 33, 34
26	Literal
27	Literal
28	ExprTuple	34, 42
29	Literal
30	ExprTuple	35, 36
31	Literal
32	Literal
33	Literal
34	Variable
35	Operation	operator: 37 operands: 38
36	Operation	operator: 39 operand: 43
37	Literal
38	ExprTuple	41, 42
39	Literal
40	ExprTuple	43
41	Literal
42	Variable
43	Literal