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, Variable, k
from proveit.logic import InSet
from proveit.numbers import Add, Exp, Mult, Neg, e, frac, i, pi, two
from proveit.physics.quantum.QPE import _b_floor, _delta_b_floor, _m_domain, _two_pow_t

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(k, Conditional(Exp(Exp(e, Mult(two, pi, i, Add(frac(_b_floor, _two_pow_t), _delta_b_floor, Neg(Variable("_a", latex_format = r"{_{-}a}"))))), k), InSet(k, _m_domain))))

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 \left(\frac{b_{\textit{f}}}{2^{t}} + \delta_{b_{\textit{f}}} - {_{-}a}\right)})^{k} \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: 10 body: 3
2	ExprTuple	10
3	Conditional	value: 4 condition: 5
4	Operation	operator: 42 operands: 6
5	Operation	operator: 7 operands: 8
6	ExprTuple	9, 10
7	Literal
8	ExprTuple	10, 11
9	Operation	operator: 42 operands: 12
10	Variable
11	Operation	operator: 13 operands: 14
12	ExprTuple	15, 16
13	Literal
14	ExprTuple	17, 18
15	Literal
16	Operation	operator: 19 operands: 20
17	Literal
18	Operation	operator: 26 operands: 21
19	Literal
20	ExprTuple	44, 22, 23, 24
21	ExprTuple	39, 25
22	Literal
23	Literal
24	Operation	operator: 26 operands: 27
25	Operation	operator: 37 operand: 32
26	Literal
27	ExprTuple	29, 30, 31
28	ExprTuple	32
29	Operation	operator: 33 operands: 34
30	Operation	operator: 35 operand: 40
31	Operation	operator: 37 operand: 41
32	Literal
33	Literal
34	ExprTuple	40, 39
35	Literal
36	ExprTuple	40
37	Literal
38	ExprTuple	41
39	Operation	operator: 42 operands: 43
40	Literal
41	Variable
42	Literal
43	ExprTuple	44, 45
44	Literal
45	Literal