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 B, Conditional, Lambda, alpha, l, n
from proveit.core_expr_types import A_1_to_l, C_1_to_n
from proveit.linear_algebra import ScalarMult
from proveit.logic import And, Equals, Forall, InClass, InSet
from proveit.numbers import Complex, Natural
from proveit.physics.quantum import Qmult, QmultCodomain

# build up the expression from sub-expressions
expr = Lambda([alpha, l, n], Conditional(Forall(instance_param_or_params = [A_1_to_l, B, C_1_to_n], instance_expr = Equals(Qmult(A_1_to_l, ScalarMult(alpha, B), C_1_to_n), Qmult(A_1_to_l, alpha, B, C_1_to_n)).with_wrapping_at(2), condition = InClass(Qmult(A_1_to_l, B, C_1_to_n), QmultCodomain)), And(InSet(alpha, Complex), InSet(l, Natural), InSet(n, Natural))))

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(\alpha, l, n\right) \mapsto \left\{\forall_{A_{1}, A_{2}, \ldots, A_{l}, B, C_{1}, C_{2}, \ldots, C_{n}~|~\left(A_{1} \thinspace  A_{2} \thinspace  \ldots \thinspace  A_{l} \thinspace B\thinspace C_{1} \thinspace  C_{2} \thinspace  \ldots \thinspace  C_{n}\right) \underset{{\scriptscriptstyle c}}{\in} \mathcal{Q^*}}~\left(\begin{array}{c} \begin{array}{l} \left(A_{1} \thinspace  A_{2} \thinspace  \ldots \thinspace  A_{l} \thinspace \left(\alpha \cdot B\right)\thinspace C_{1} \thinspace  C_{2} \thinspace  \ldots \thinspace  C_{n}\right) =  \\ \left(A_{1} \thinspace  A_{2} \thinspace  \ldots \thinspace  A_{l} \thinspace \alpha \thinspace B\thinspace C_{1} \thinspace  C_{2} \thinspace  \ldots \thinspace  C_{n}\right) \end{array} \end{array}\right) \textrm{ if } \alpha \in \mathbb{C} ,  l \in \mathbb{N} ,  n \in \mathbb{N}\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	44, 40, 43
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 9
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9
7	Literal
8	ExprTuple	10, 11, 12
9	Lambda	parameters: 33 body: 13
10	Operation	operator: 16 operands: 14
11	Operation	operator: 16 operands: 15
12	Operation	operator: 16 operands: 17
13	Conditional	value: 18 condition: 19
14	ExprTuple	44, 20
15	ExprTuple	40, 21
16	Literal
17	ExprTuple	43, 21
18	Operation	operator: 22 operands: 23
19	Operation	operator: 24 operands: 25
20	Literal
21	Literal
22	Literal
23	ExprTuple	26, 27
24	Literal
25	ExprTuple	28, 29
26	Operation	operator: 32 operands: 30
27	Operation	operator: 32 operands: 31
28	Operation	operator: 32 operands: 33
29	Literal
30	ExprTuple	35, 34, 36
31	ExprTuple	35, 44, 45, 36
32	Literal
33	ExprTuple	35, 45, 36
34	Operation	operator: 37 operands: 38
35	ExprRange	lambda_map: 39 start_index: 42 end_index: 40
36	ExprRange	lambda_map: 41 start_index: 42 end_index: 43
37	Literal
38	ExprTuple	44, 45
39	Lambda	parameter: 51 body: 46
40	Variable
41	Lambda	parameter: 51 body: 47
42	Literal
43	Variable
44	Variable
45	Variable
46	IndexedVar	variable: 48 index: 51
47	IndexedVar	variable: 49 index: 51
48	Variable
49	Variable
50	ExprTuple	51
51	Variable