Expression of type Conditional

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, m, n, x
from proveit.linear_algebra import MatrixMult, MatrixSpace
from proveit.logic import CartExp, Equals, InSet
from proveit.numbers import Complex
from proveit.physics.quantum import Qmult

# build up the expression from sub-expressions
expr = Conditional(Equals(Qmult(M), Lambda(x, Conditional(MatrixMult(M, x), InSet(x, CartExp(Complex, n))))), InSet(M, MatrixSpace(field = Complex, rows = m, columns = n)))

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\{\left[M\right] = \left[x \mapsto \left\{M \thinspace x \textrm{ if } x \in \mathbb{C}^{n}\right..\right] \textrm{ if } M \in \mathbb{C}^{m \times n}\right..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Conditional	value: 1 condition: 2
1	Operation	operator: 3 operands: 4
2	Operation	operator: 20 operands: 5
3	Literal
4	ExprTuple	6, 7
5	ExprTuple	22, 8
6	Operation	operator: 9 operand: 22
7	Lambda	parameter: 23 body: 12
8	Operation	operator: 13 operands: 14
9	Literal
10	ExprTuple	22
11	ExprTuple	23
12	Conditional	value: 15 condition: 16
13	Literal
14	NamedExprs	field: 27 rows: 17 columns: 28
15	Operation	operator: 18 operands: 19
16	Operation	operator: 20 operands: 21
17	Variable
18	Literal
19	ExprTuple	22, 23
20	Literal
21	ExprTuple	23, 24
22	Variable
23	Variable
24	Operation	operator: 25 operands: 26
25	Literal
26	ExprTuple	27, 28
27	Literal
28	Variable