Expression of type ExprTuple

from the theory of proveit.physics.quantum.algebra

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, ExprRange, ExprTuple, Function, IndexedVar, Lambda, Variable, a, f, i, n
from proveit.core_expr_types import a_1_to_n, a_i, v_i
from proveit.linear_algebra import ScalarMult, VecSum
from proveit.logic import And, Equals, Forall, Functions, InSet
from proveit.numbers import Complex, Interval, one
from proveit.physics.quantum import Bra, Ket, Qmult

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = [i]
sub_expr3 = Interval(one, n)
sub_expr4 = Qmult(Ket(v_i), Bra(v_i))
expr = ExprTuple(Lambda([a_1_to_n], Conditional(Forall(instance_param_or_params = [f], instance_expr = Equals(Function(f, [VecSum(index_or_indices = sub_expr2, summand = ScalarMult(a_i, sub_expr4), domain = sub_expr3)]), VecSum(index_or_indices = sub_expr2, summand = ScalarMult(Function(f, [a_i]), sub_expr4), domain = sub_expr3)), domain = Functions(Complex, Complex)), And(ExprRange(sub_expr1, InSet(IndexedVar(a, sub_expr1), Complex), one, n)))))

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(\left(a_{1}, a_{2}, \ldots, a_{n}\right) \mapsto \left\{\forall_{f \in \left[\mathbb{C} \rightarrow \mathbb{C}\right]}~\left(f\left(\sum_{i=1}^{n} \left(a_{i} \cdot \left(\lvert v_{i} \rangle \thinspace \langle v_{i} \rvert\right)\right)\right) = \left(\sum_{i=1}^{n} \left(f\left(a_{i}\right) \cdot \left(\lvert v_{i} \rangle \thinspace \langle v_{i} \rvert\right)\right)\right)\right) \textrm{ if } \left(a_{1} \in \mathbb{C}\right) \land  \left(a_{2} \in \mathbb{C}\right) \land  \ldots \land  \left(a_{n} \in \mathbb{C}\right)\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	parameters: 2 body: 3
2	ExprTuple	4
3	Conditional	value: 5 condition: 6
4	ExprRange	lambda_map: 7 start_index: 63 end_index: 64
5	Operation	operator: 8 operand: 12
6	Operation	operator: 10 operands: 11
7	Lambda	parameter: 36 body: 27
8	Literal
9	ExprTuple	12
10	Literal
11	ExprTuple	13
12	Lambda	parameter: 51 body: 15
13	ExprRange	lambda_map: 16 start_index: 63 end_index: 64
14	ExprTuple	51
15	Conditional	value: 17 condition: 18
16	Lambda	parameter: 36 body: 19
17	Operation	operator: 20 operands: 21
18	Operation	operator: 49 operands: 22
19	Operation	operator: 49 operands: 23
20	Literal
21	ExprTuple	24, 25
22	ExprTuple	51, 26
23	ExprTuple	27, 35
24	Operation	operator: 51 operand: 33
25	Operation	operator: 37 operand: 34
26	Operation	operator: 30 operands: 31
27	IndexedVar	variable: 60 index: 36
28	ExprTuple	33
29	ExprTuple	34
30	Literal
31	ExprTuple	35, 35
32	ExprTuple	36
33	Operation	operator: 37 operand: 40
34	Lambda	parameter: 71 body: 39
35	Literal
36	Variable
37	Literal
38	ExprTuple	40
39	Conditional	value: 41 condition: 45
40	Lambda	parameter: 71 body: 42
41	Operation	operator: 47 operands: 43
42	Conditional	value: 44 condition: 45
43	ExprTuple	46, 53
44	Operation	operator: 47 operands: 48
45	Operation	operator: 49 operands: 50
46	Operation	operator: 51 operand: 55
47	Literal
48	ExprTuple	55, 53
49	Literal
50	ExprTuple	71, 54
51	Variable
52	ExprTuple	55
53	Operation	operator: 56 operands: 57
54	Operation	operator: 58 operands: 59
55	IndexedVar	variable: 60 index: 71
56	Literal
57	ExprTuple	61, 62
58	Literal
59	ExprTuple	63, 64
60	Variable
61	Operation	operator: 65 operand: 68
62	Operation	operator: 66 operand: 68
63	Literal
64	Variable
65	Literal
66	Literal
67	ExprTuple	68
68	IndexedVar	variable: 69 index: 71
69	Variable
70	ExprTuple	71
71	Variable