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, ExprRange, IndexedVar, Lambda, Variable, b, j
from proveit.core_expr_types import A_1_to_l, C_1_to_n, b_1_to_j
from proveit.logic import And, Equals, Forall, InClass, InSet
from proveit.numbers import Complex, one
from proveit.physics.quantum import Qmult, QmultCodomain

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Lambda([b_1_to_j], Conditional(Forall(instance_param_or_params = [A_1_to_l, C_1_to_n], instance_expr = Equals(Qmult(A_1_to_l, b_1_to_j, C_1_to_n), Qmult(b_1_to_j, A_1_to_l, C_1_to_n)).with_wrapping_at(2), condition = InClass(Qmult(A_1_to_l, C_1_to_n), QmultCodomain)), And(ExprRange(sub_expr1, InSet(IndexedVar(b, sub_expr1), Complex), one, j))))

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(b_{1}, b_{2}, \ldots, b_{j}\right) \mapsto \left\{\forall_{A_{1}, A_{2}, \ldots, A_{l}, C_{1}, C_{2}, \ldots, C_{n}~|~\left(A_{1} \thinspace  A_{2} \thinspace  \ldots \thinspace  A_{l}\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 b_{1} \thinspace  b_{2} \thinspace  \ldots \thinspace  b_{j}\thinspace C_{1} \thinspace  C_{2} \thinspace  \ldots \thinspace  C_{n}\right) =  \\ \left(b_{1} \thinspace  b_{2} \thinspace  \ldots \thinspace  b_{j}\thinspace A_{1} \thinspace  A_{2} \thinspace  \ldots \thinspace  A_{l}\thinspace C_{1} \thinspace  C_{2} \thinspace  \ldots \thinspace  C_{n}\right) \end{array} \end{array}\right) \textrm{ if } \left(b_{1} \in \mathbb{C}\right) \land  \left(b_{2} \in \mathbb{C}\right) \land  \ldots \land  \left(b_{j} \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	31
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
9	Lambda	parameters: 30 body: 11
10	ExprRange	lambda_map: 12 start_index: 39 end_index: 35
11	Conditional	value: 13 condition: 14
12	Lambda	parameter: 48 body: 15
13	Operation	operator: 16 operands: 17
14	Operation	operator: 18 operands: 19
15	Operation	operator: 20 operands: 21
16	Literal
17	ExprTuple	22, 23
18	Literal
19	ExprTuple	24, 25
20	Literal
21	ExprTuple	41, 26
22	Operation	operator: 29 operands: 27
23	Operation	operator: 29 operands: 28
24	Operation	operator: 29 operands: 30
25	Literal
26	Literal
27	ExprTuple	32, 31, 33
28	ExprTuple	31, 32, 33
29	Literal
30	ExprTuple	32, 33
31	ExprRange	lambda_map: 34 start_index: 39 end_index: 35
32	ExprRange	lambda_map: 36 start_index: 39 end_index: 37
33	ExprRange	lambda_map: 38 start_index: 39 end_index: 40
34	Lambda	parameter: 48 body: 41
35	Variable
36	Lambda	parameter: 48 body: 42
37	Variable
38	Lambda	parameter: 48 body: 43
39	Literal
40	Variable
41	IndexedVar	variable: 44 index: 48
42	IndexedVar	variable: 45 index: 48
43	IndexedVar	variable: 46 index: 48
44	Variable
45	Variable
46	Variable
47	ExprTuple	48
48	Variable