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 Conditional, Lambda
from proveit.core_expr_types import A_1_to_l, b_1_to_j
from proveit.logic import Equals, InClass
from proveit.numbers import Mult
from proveit.physics.quantum import Qmult, QmultCodomain

# build up the expression from sub-expressions
expr = Lambda([A_1_to_l], Conditional(Equals(Qmult(b_1_to_j, A_1_to_l), Qmult(Mult(b_1_to_j), A_1_to_l)).with_wrapping_at(2), InClass(Qmult(A_1_to_l), QmultCodomain)))

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_{l}\right) \mapsto \left\{\begin{array}{c} \begin{array}{l} \left(b_{1} \thinspace  b_{2} \thinspace  \ldots \thinspace  b_{j}\thinspace A_{1} \thinspace  A_{2} \thinspace  \ldots \thinspace  A_{l}\right) =  \\ \left(\left(b_{1} \cdot  b_{2} \cdot  \ldots \cdot  b_{j}\right)\thinspace A_{1} \thinspace  A_{2} \thinspace  \ldots \thinspace  A_{l}\right) \end{array} \end{array} \textrm{ if } \left(A_{1} \thinspace  A_{2} \thinspace  \ldots \thinspace  A_{l}\right) \underset{{\scriptscriptstyle c}}{\in} \mathcal{Q^*}\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 15 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 4 operands: 5
3	Operation	operator: 6 operands: 7
4	Literal
5	ExprTuple	8, 9
6	Literal
7	ExprTuple	10, 11
8	Operation	operator: 14 operands: 12
9	Operation	operator: 14 operands: 13
10	Operation	operator: 14 operands: 15
11	Literal
12	ExprTuple	22, 17
13	ExprTuple	16, 17
14	Literal
15	ExprTuple	17
16	Operation	operator: 18 operands: 19
17	ExprRange	lambda_map: 20 start_index: 25 end_index: 21
18	Literal
19	ExprTuple	22
20	Lambda	parameter: 31 body: 23
21	Variable
22	ExprRange	lambda_map: 24 start_index: 25 end_index: 26
23	IndexedVar	variable: 27 index: 31
24	Lambda	parameter: 31 body: 28
25	Literal
26	Variable
27	Variable
28	IndexedVar	variable: 29 index: 31
29	Variable
30	ExprTuple	31
31	Variable