Expression of type ExprTuple

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, ExprTuple, 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 = ExprTuple(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(\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..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameters: 2 body: 3
2	ExprTuple	39, 37
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 10
5	Operation	operator: 8 operands: 9
6	Literal
7	ExprTuple	10
8	Literal
9	ExprTuple	11, 12
10	Lambda	parameter: 31 body: 13
11	Operation	operator: 20 operands: 14
12	Operation	operator: 20 operands: 15
13	Conditional	value: 16 condition: 17
14	ExprTuple	39, 18
15	ExprTuple	37, 18
16	Operation	operator: 20 operands: 19
17	Operation	operator: 20 operands: 21
18	Literal
19	ExprTuple	22, 23
20	Literal
21	ExprTuple	31, 24
22	Operation	operator: 25 operand: 31
23	Operation	operator: 27 operands: 28
24	Operation	operator: 29 operands: 30
25	Literal
26	ExprTuple	31
27	Literal
28	ExprTuple	32, 33
29	Literal
30	NamedExprs	field: 38 rows: 39 columns: 37
31	Variable
32	Operation	operator: 35 operands: 34
33	Operation	operator: 35 operands: 36
34	ExprTuple	38, 37
35	Literal
36	ExprTuple	38, 39
37	Variable
38	Literal
39	Variable