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

no style options

# display the expression information
stored_expr.expr_info()

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