Expression of type Lambda

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 A, B, Conditional, ExprRange, IndexedVar, Lambda, Variable, a, b, i, n
from proveit.core_expr_types import a_1_to_n, a_i, b_1_to_n, b_i, v_i
from proveit.linear_algebra import ScalarMult, VecSum
from proveit.logic import And, Equals, 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 = Lambda([a_1_to_n, b_1_to_n], Conditional(And(Equals(A, VecSum(index_or_indices = sub_expr2, summand = ScalarMult(a_i, sub_expr4), domain = sub_expr3)), Equals(B, VecSum(index_or_indices = sub_expr2, summand = ScalarMult(b_i, sub_expr4), domain = sub_expr3))).with_wrapping_at(2), And(ExprRange(sub_expr1, InSet(IndexedVar(a, sub_expr1), Complex), one, n), ExprRange(sub_expr1, InSet(IndexedVar(b, 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(a_{1}, a_{2}, \ldots, a_{n}, b_{1}, b_{2}, \ldots, b_{n}\right) \mapsto \left\{\begin{array}{c} \left(A = \left(\sum_{i=1}^{n} \left(a_{i} \cdot \left(\lvert v_{i} \rangle \thinspace \langle v_{i} \rvert\right)\right)\right)\right) \land  \\ \left(B = \left(\sum_{i=1}^{n} \left(b_{i} \cdot \left(\lvert v_{i} \rangle \thinspace \langle v_{i} \rvert\right)\right)\right)\right) \end{array} \textrm{ if } \left(a_{1} \in \mathbb{C}\right) ,  \left(a_{2} \in \mathbb{C}\right) ,  \ldots ,  \left(a_{n} \in \mathbb{C}\right), \left(b_{1} \in \mathbb{C}\right) ,  \left(b_{2} \in \mathbb{C}\right) ,  \ldots ,  \left(b_{n} \in \mathbb{C}\right)\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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