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 And, CartExp, Equals, 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 = Equals(Qmult(M), Lambda(x, Conditional(MatrixMult(M, x), InSet(x, CartExp(Complex, n))))), 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] = \left[x \mapsto \left\{M \thinspace x \textrm{ if } x \in \mathbb{C}^{n}\right..\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: 35 body: 10
8	Operation	operator: 33 operands: 11
9	Operation	operator: 33 operands: 12
10	Conditional	value: 13 condition: 14
11	ExprTuple	30, 15
12	ExprTuple	41, 15
13	Operation	operator: 16 operands: 17
14	Operation	operator: 33 operands: 18
15	Literal
16	Literal
17	ExprTuple	19, 20
18	ExprTuple	35, 21
19	Operation	operator: 22 operand: 35
20	Lambda	parameter: 36 body: 25
21	Operation	operator: 26 operands: 27
22	Literal
23	ExprTuple	35
24	ExprTuple	36
25	Conditional	value: 28 condition: 29
26	Literal
27	NamedExprs	field: 40 rows: 30 columns: 41
28	Operation	operator: 31 operands: 32
29	Operation	operator: 33 operands: 34
30	Variable
31	Literal
32	ExprTuple	35, 36
33	Literal
34	ExprTuple	36, 37
35	Variable
36	Variable
37	Operation	operator: 38 operands: 39
38	Literal
39	ExprTuple	40, 41
40	Literal
41	Variable