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 Equals, Forall, InSet
from proveit.numbers import Add, 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
sub_expr1 = Add(k, two_pow_t)
sub_expr2 = Interval(zero, subtract(two_pow_t, one))
sub_expr3 = InSet(k, sub_expr2)
sub_expr4 = ScalarMult(Exp(e, Mult(two, pi, i, _phase, sub_expr1)), NumKet(sub_expr1, Add(t, one)))
sub_expr5 = ScalarMult(Mult(Exp(e, Mult(two, pi, i, _phase, k)), Exp(e, Mult(two, pi, i, _phase, two_pow_t))), TensorProd(ket1, NumKet(k, t)))
expr = ExprTuple(Forall(instance_param_or_params = [k], instance_expr = Equals(sub_expr4, sub_expr5), domain = sub_expr2), Equals(Lambda(k, Conditional(sub_expr4, sub_expr3)), Lambda(k, Conditional(sub_expr5, sub_expr3))).with_wrapping_at(2))

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(\forall_{k \in \{0~\ldotp \ldotp~2^{t} - 1\}}~\left(\left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot \left(k + 2^{t}\right)} \cdot \lvert k + 2^{t} \rangle_{t + 1}\right) = \left(\left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot k} \cdot \mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot 2^{t}}\right) \cdot \left(\lvert 1 \rangle {\otimes} \lvert k \rangle_{t}\right)\right)\right), \begin{array}{c} \begin{array}{l} \left[k \mapsto \left\{\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot \left(k + 2^{t}\right)} \cdot \lvert k + 2^{t} \rangle_{t + 1} \textrm{ if } k \in \{0~\ldotp \ldotp~2^{t} - 1\}\right..\right] =  \\ \left[k \mapsto \left\{\left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot k} \cdot \mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot 2^{t}}\right) \cdot \left(\lvert 1 \rangle {\otimes} \lvert k \rangle_{t}\right) \textrm{ if } k \in \{0~\ldotp \ldotp~2^{t} - 1\}\right..\right] \end{array} \end{array}\right)

stored_expr.style_options()

name	description	default	current value	related methods
wrap_positions	position(s) at which wrapping is to occur; 'n' is after the nth comma.	()	()	('with_wrapping_at',)
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	left	left	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1, 2
1	Operation	operator: 3 operand: 6
2	Operation	operator: 15 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	7, 8
6	Lambda	parameter: 65 body: 9
7	Lambda	parameter: 65 body: 10
8	Lambda	parameter: 65 body: 12
9	Conditional	value: 13 condition: 14
10	Conditional	value: 19 condition: 14
11	ExprTuple	65
12	Conditional	value: 20 condition: 14
13	Operation	operator: 15 operands: 16
14	Operation	operator: 17 operands: 18
15	Literal
16	ExprTuple	19, 20
17	Literal
18	ExprTuple	65, 21
19	Operation	operator: 23 operands: 22
20	Operation	operator: 23 operands: 24
21	Operation	operator: 25 operands: 26
22	ExprTuple	27, 28
23	Literal
24	ExprTuple	29, 30
25	Literal
26	ExprTuple	31, 32
27	Operation	operator: 70 operands: 33
28	Operation	operator: 51 operands: 34
29	Operation	operator: 63 operands: 35
30	Operation	operator: 36 operands: 37
31	Literal
32	Operation	operator: 60 operands: 38
33	ExprTuple	57, 39
34	ExprTuple	55, 40
35	ExprTuple	41, 42
36	Literal
37	ExprTuple	43, 44
38	ExprTuple	69, 45
39	Operation	operator: 63 operands: 46
40	Operation	operator: 60 operands: 47
41	Operation	operator: 70 operands: 48
42	Operation	operator: 70 operands: 49
43	Operation	operator: 50 operand: 59
44	Operation	operator: 51 operands: 52
45	Operation	operator: 53 operand: 59
46	ExprTuple	72, 66, 67, 68, 55
47	ExprTuple	73, 59
48	ExprTuple	57, 56
49	ExprTuple	57, 58
50	Literal
51	Literal
52	ExprTuple	65, 73
53	Literal
54	ExprTuple	59
55	Operation	operator: 60 operands: 61
56	Operation	operator: 63 operands: 62
57	Literal
58	Operation	operator: 63 operands: 64
59	Literal
60	Literal
61	ExprTuple	65, 69
62	ExprTuple	72, 66, 67, 68, 65
63	Literal
64	ExprTuple	72, 66, 67, 68, 69
65	Variable
66	Literal
67	Literal
68	Literal
69	Operation	operator: 70 operands: 71
70	Literal
71	ExprTuple	72, 73
72	Literal
73	Variable