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, a
from proveit.core_expr_types import B_1_to_j
from proveit.linear_algebra import ScalarMult
from proveit.logic import Equals, Forall, InClass, InSet
from proveit.numbers import Complex
from proveit.physics.quantum import Qmult, QmultCodomain

# build up the expression from sub-expressions
sub_expr1 = Qmult(B_1_to_j)
expr = Lambda(a, Conditional(Forall(instance_param_or_params = [B_1_to_j], instance_expr = Equals(Qmult(a, B_1_to_j), ScalarMult(a, sub_expr1)).with_wrapping_at(2), condition = InClass(sub_expr1, QmultCodomain)), InSet(a, Complex)))

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())

a \mapsto \left\{\forall_{B_{1}, B_{2}, \ldots, B_{j}~|~\left(B_{1} \thinspace  B_{2} \thinspace  \ldots \thinspace  B_{j}\right) \underset{{\scriptscriptstyle c}}{\in} \mathcal{Q^*}}~\left(\begin{array}{c} \begin{array}{l} \left(a\thinspace B_{1} \thinspace  B_{2} \thinspace  \ldots \thinspace  B_{j}\right) =  \\ \left(a \cdot \left(B_{1} \thinspace  B_{2} \thinspace  \ldots \thinspace  B_{j}\right)\right) \end{array} \end{array}\right) \textrm{ if } a \in \mathbb{C}\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 24 body: 2
1	ExprTuple	24
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	24, 10
9	Lambda	parameters: 27 body: 11
10	Literal
11	Conditional	value: 12 condition: 13
12	Operation	operator: 14 operands: 15
13	Operation	operator: 16 operands: 17
14	Literal
15	ExprTuple	18, 19
16	Literal
17	ExprTuple	25, 20
18	Operation	operator: 26 operands: 21
19	Operation	operator: 22 operands: 23
20	Literal
21	ExprTuple	24, 28
22	Literal
23	ExprTuple	24, 25
24	Variable
25	Operation	operator: 26 operands: 27
26	Literal
27	ExprTuple	28
28	ExprRange	lambda_map: 29 start_index: 30 end_index: 31
29	Lambda	parameter: 35 body: 32
30	Literal
31	Variable
32	IndexedVar	variable: 33 index: 35
33	Variable
34	ExprTuple	35
35	Variable