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_m, C_1_to_n
from proveit.logic import Equals, InClass
from proveit.physics.quantum import Qmult, QmultCodomain

# build up the expression from sub-expressions
sub_expr1 = Qmult(A_1_to_l, B_1_to_m, C_1_to_n)
expr = Lambda([A_1_to_l, B_1_to_m, C_1_to_n], Conditional(Equals(Qmult(A_1_to_l, Qmult(B_1_to_m), C_1_to_n), sub_expr1).with_wrapping_at(2), InClass(sub_expr1, 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}, B_{1}, B_{2}, \ldots, B_{m}, C_{1}, C_{2}, \ldots, C_{n}\right) \mapsto \left\{\begin{array}{c} \begin{array}{l} \left(A_{1} \thinspace  A_{2} \thinspace  \ldots \thinspace  A_{l} \thinspace \left(B_{1} \thinspace  B_{2} \thinspace  \ldots \thinspace  B_{m}\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 B_{1} \thinspace  B_{2} \thinspace  \ldots \thinspace  B_{m}\thinspace C_{1} \thinspace  C_{2} \thinspace  \ldots \thinspace  C_{n}\right) \end{array} \end{array} \textrm{ if } \left(A_{1} \thinspace  A_{2} \thinspace  \ldots \thinspace  A_{l}\thinspace B_{1} \thinspace  B_{2} \thinspace  \ldots \thinspace  B_{m}\thinspace C_{1} \thinspace  C_{2} \thinspace  \ldots \thinspace  C_{n}\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: 12 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	9, 10
8	Operation	operator: 16 operands: 11
9	Operation	operator: 16 operands: 12
10	Literal
11	ExprTuple	14, 13, 15
12	ExprTuple	14, 22, 15
13	Operation	operator: 16 operands: 17
14	ExprRange	lambda_map: 18 start_index: 26 end_index: 19
15	ExprRange	lambda_map: 20 start_index: 26 end_index: 21
16	Literal
17	ExprTuple	22
18	Lambda	parameter: 33 body: 23
19	Variable
20	Lambda	parameter: 33 body: 24
21	Variable
22	ExprRange	lambda_map: 25 start_index: 26 end_index: 27
23	IndexedVar	variable: 28 index: 33
24	IndexedVar	variable: 29 index: 33
25	Lambda	parameter: 33 body: 30
26	Literal
27	Variable
28	Variable
29	Variable
30	IndexedVar	variable: 31 index: 33
31	Variable
32	ExprTuple	33
33	Variable