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 ExprRange, ExprTuple, Variable, t
from proveit.linear_algebra import ScalarMult, VecAdd
from proveit.logic import And, CartExp, Forall, InSet
from proveit.numbers import Add, Complex, Exp, Interval, Mult, Neg, e, frac, i, one, pi, sqrt, two, zero
from proveit.physics.quantum import ket0, ket1
from proveit.physics.quantum.QPE import _phase

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = Add(Neg(t), two)
sub_expr3 = InSet(ScalarMult(frac(one, sqrt(two)), VecAdd(ket0, ScalarMult(Exp(e, Mult(two, pi, i, Exp(two, Neg(sub_expr1)), _phase)), ket1))), CartExp(Complex, Exp(two, one)))
expr = ExprTuple(Forall(instance_param_or_params = [sub_expr1], instance_expr = sub_expr3, domain = Interval(sub_expr2, zero)), And(ExprRange(sub_expr1, sub_expr3, sub_expr2, zero)))

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_{{_{-}a} \in \{-t + 2~\ldotp \ldotp~0\}}~\left(\left(\frac{1}{\sqrt{2}} \cdot \left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot 2^{-{_{-}a}} \cdot \varphi} \cdot \lvert 1 \rangle\right)\right)\right) \in \mathbb{C}^{2^{1}}\right), \left(\left(\frac{1}{\sqrt{2}} \cdot \left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot 2^{-\left(-t + 2\right)} \cdot \varphi} \cdot \lvert 1 \rangle\right)\right)\right) \in \mathbb{C}^{2^{1}}\right) \land  \left(\left(\frac{1}{\sqrt{2}} \cdot \left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot 2^{-\left(-t + 3\right)} \cdot \varphi} \cdot \lvert 1 \rangle\right)\right)\right) \in \mathbb{C}^{2^{1}}\right) \land  \ldots \land  \left(\left(\frac{1}{\sqrt{2}} \cdot \left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot 2^{-0} \cdot \varphi} \cdot \lvert 1 \rangle\right)\right)\right) \in \mathbb{C}^{2^{1}}\right)\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: 7
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7
5	Literal
6	ExprTuple	8
7	Lambda	parameter: 69 body: 9
8	ExprRange	lambda_map: 10 start_index: 24 end_index: 46
9	Conditional	value: 12 condition: 11
10	Lambda	parameter: 69 body: 12
11	Operation	operator: 14 operands: 13
12	Operation	operator: 14 operands: 15
13	ExprTuple	69, 16
14	Literal
15	ExprTuple	17, 18
16	Operation	operator: 19 operands: 20
17	Operation	operator: 42 operands: 21
18	Operation	operator: 22 operands: 23
19	Literal
20	ExprTuple	24, 46
21	ExprTuple	25, 26
22	Literal
23	ExprTuple	27, 28
24	Operation	operator: 29 operands: 30
25	Operation	operator: 49 operands: 31
26	Operation	operator: 32 operands: 33
27	Literal
28	Operation	operator: 63 operands: 34
29	Literal
30	ExprTuple	35, 65
31	ExprTuple	56, 36
32	Literal
33	ExprTuple	37, 38
34	ExprTuple	65, 56
35	Operation	operator: 67 operand: 44
36	Operation	operator: 63 operands: 40
37	Operation	operator: 52 operand: 46
38	Operation	operator: 42 operands: 43
39	ExprTuple	44
40	ExprTuple	65, 45
41	ExprTuple	46
42	Literal
43	ExprTuple	47, 48
44	Variable
45	Operation	operator: 49 operands: 50
46	Literal
47	Operation	operator: 63 operands: 51
48	Operation	operator: 52 operand: 56
49	Literal
50	ExprTuple	56, 65
51	ExprTuple	54, 55
52	Literal
53	ExprTuple	56
54	Literal
55	Operation	operator: 57 operands: 58
56	Literal
57	Literal
58	ExprTuple	65, 59, 60, 61, 62
59	Literal
60	Literal
61	Operation	operator: 63 operands: 64
62	Literal
63	Literal
64	ExprTuple	65, 66
65	Literal
66	Operation	operator: 67 operand: 69
67	Literal
68	ExprTuple	69
69	Variable