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, 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 = ExprTuple(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(\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..\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	33, 44
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: 38 body: 13
11	Operation	operator: 36 operands: 14
12	Operation	operator: 36 operands: 15
13	Conditional	value: 16 condition: 17
14	ExprTuple	33, 18
15	ExprTuple	44, 18
16	Operation	operator: 19 operands: 20
17	Operation	operator: 36 operands: 21
18	Literal
19	Literal
20	ExprTuple	22, 23
21	ExprTuple	38, 24
22	Operation	operator: 25 operand: 38
23	Lambda	parameter: 39 body: 28
24	Operation	operator: 29 operands: 30
25	Literal
26	ExprTuple	38
27	ExprTuple	39
28	Conditional	value: 31 condition: 32
29	Literal
30	NamedExprs	field: 43 rows: 33 columns: 44
31	Operation	operator: 34 operands: 35
32	Operation	operator: 36 operands: 37
33	Variable
34	Literal
35	ExprTuple	38, 39
36	Literal
37	ExprTuple	39, 40
38	Variable
39	Variable
40	Operation	operator: 41 operands: 42
41	Literal
42	ExprTuple	43, 44
43	Literal
44	Variable