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, m, n
from proveit.core_expr_types import Q__b_1_to_j, b_1_to_j, f__b_1_to_j
from proveit.linear_algebra import MatrixSpace
from proveit.logic import InSet
from proveit.numbers import Complex

# build up the expression from sub-expressions
expr = Lambda([b_1_to_j], Conditional(InSet(f__b_1_to_j, MatrixSpace(field = Complex, rows = n, columns = m)), Q__b_1_to_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\{f\left(b_{1}, b_{2}, \ldots, b_{j}\right) \in \mathbb{C}^{n \times m} \textrm{ if } Q\left(b_{1}, b_{2}, \ldots, b_{j}\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: 10 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 4 operands: 5
3	Operation	operator: 6 operands: 10
4	Literal
5	ExprTuple	7, 8
6	Variable
7	Operation	operator: 9 operands: 10
8	Operation	operator: 11 operands: 12
9	Variable
10	ExprTuple	13
11	Literal
12	NamedExprs	field: 14 rows: 15 columns: 16
13	ExprRange	lambda_map: 17 start_index: 18 end_index: 19
14	Literal
15	Variable
16	Variable
17	Lambda	parameter: 23 body: 20
18	Literal
19	Variable
20	IndexedVar	variable: 21 index: 23
21	Variable
22	ExprTuple	23
23	Variable