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, 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 = Lambda([m, n], 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(m, n\right) \mapsto \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()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 1 body: 2
1	ExprTuple	32, 43
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	10, 11
9	Lambda	parameter: 37 body: 12
10	Operation	operator: 35 operands: 13
11	Operation	operator: 35 operands: 14
12	Conditional	value: 15 condition: 16
13	ExprTuple	32, 17
14	ExprTuple	43, 17
15	Operation	operator: 18 operands: 19
16	Operation	operator: 35 operands: 20
17	Literal
18	Literal
19	ExprTuple	21, 22
20	ExprTuple	37, 23
21	Operation	operator: 24 operand: 37
22	Lambda	parameter: 38 body: 27
23	Operation	operator: 28 operands: 29
24	Literal
25	ExprTuple	37
26	ExprTuple	38
27	Conditional	value: 30 condition: 31
28	Literal
29	NamedExprs	field: 42 rows: 32 columns: 43
30	Operation	operator: 33 operands: 34
31	Operation	operator: 35 operands: 36
32	Variable
33	Literal
34	ExprTuple	37, 38
35	Literal
36	ExprTuple	38, 39
37	Variable
38	Variable
39	Operation	operator: 40 operands: 41
40	Literal
41	ExprTuple	42, 43
42	Literal
43	Variable