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, M, m, n
from proveit.linear_algebra import LinMap, MatrixSpace
from proveit.logic import And, CartExp, Forall, InSet
from proveit.numbers import Complex, NaturalPos
from proveit.physics.quantum import Qmult

# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [M], instance_expr = InSet(Qmult(M), LinMap(CartExp(Complex, n), CartExp(Complex, m))), domain = MatrixSpace(field = Complex, rows = m, columns = n)), And(InSet(m, NaturalPos), InSet(n, NaturalPos)))

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\{\forall_{M \in \mathbb{C}^{m \times n}}~\left(\left[M\right] \in \mathcal{L}\left(\mathbb{C}^{n}, \mathbb{C}^{m}\right)\right) \textrm{ if } m \in \mathbb{N}^+ ,  n \in \mathbb{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 operand: 7
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7
5	Literal
6	ExprTuple	8, 9
7	Lambda	parameter: 28 body: 10
8	Operation	operator: 17 operands: 11
9	Operation	operator: 17 operands: 12
10	Conditional	value: 13 condition: 14
11	ExprTuple	36, 15
12	ExprTuple	34, 15
13	Operation	operator: 17 operands: 16
14	Operation	operator: 17 operands: 18
15	Literal
16	ExprTuple	19, 20
17	Literal
18	ExprTuple	28, 21
19	Operation	operator: 22 operand: 28
20	Operation	operator: 24 operands: 25
21	Operation	operator: 26 operands: 27
22	Literal
23	ExprTuple	28
24	Literal
25	ExprTuple	29, 30
26	Literal
27	NamedExprs	field: 35 rows: 36 columns: 34
28	Variable
29	Operation	operator: 32 operands: 31
30	Operation	operator: 32 operands: 33
31	ExprTuple	35, 34
32	Literal
33	ExprTuple	35, 36
34	Variable
35	Literal
36	Variable