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 Norm, ScalarMult, VecAdd
from proveit.logic import And, Equals, Forall
from proveit.numbers import Add, 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), one)
sub_expr3 = Equals(Norm(ScalarMult(frac(one, sqrt(two)), VecAdd(ket0, ScalarMult(Exp(e, Mult(two, pi, i, Exp(two, Neg(sub_expr1)), _phase)), ket1)))), 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 + 1~\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 \| = 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 + 1\right)} \cdot \varphi} \cdot \lvert 1 \rangle\right)\right)\right \| = 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 + 2\right)} \cdot \varphi} \cdot \lvert 1 \rangle\right)\right)\right \| = 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 \| = 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: 67 body: 9
8	ExprRange	lambda_map: 10 start_index: 23 end_index: 44
9	Conditional	value: 12 condition: 11
10	Lambda	parameter: 67 body: 12
11	Operation	operator: 13 operands: 14
12	Operation	operator: 15 operands: 16
13	Literal
14	ExprTuple	67, 17
15	Literal
16	ExprTuple	18, 54
17	Operation	operator: 19 operands: 20
18	Operation	operator: 21 operand: 24
19	Literal
20	ExprTuple	23, 44
21	Literal
22	ExprTuple	24
23	Operation	operator: 25 operands: 26
24	Operation	operator: 41 operands: 27
25	Literal
26	ExprTuple	28, 54
27	ExprTuple	29, 30
28	Operation	operator: 65 operand: 35
29	Operation	operator: 47 operands: 32
30	Operation	operator: 33 operands: 34
31	ExprTuple	35
32	ExprTuple	54, 36
33	Literal
34	ExprTuple	37, 38
35	Variable
36	Operation	operator: 61 operands: 39
37	Operation	operator: 50 operand: 44
38	Operation	operator: 41 operands: 42
39	ExprTuple	63, 43
40	ExprTuple	44
41	Literal
42	ExprTuple	45, 46
43	Operation	operator: 47 operands: 48
44	Literal
45	Operation	operator: 61 operands: 49
46	Operation	operator: 50 operand: 54
47	Literal
48	ExprTuple	54, 63
49	ExprTuple	52, 53
50	Literal
51	ExprTuple	54
52	Literal
53	Operation	operator: 55 operands: 56
54	Literal
55	Literal
56	ExprTuple	63, 57, 58, 59, 60
57	Literal
58	Literal
59	Operation	operator: 61 operands: 62
60	Literal
61	Literal
62	ExprTuple	63, 64
63	Literal
64	Operation	operator: 65 operand: 67
65	Literal
66	ExprTuple	67
67	Variable