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 MatrixSpace
from proveit.logic import And, Forall, InClass, InSet
from proveit.numbers import Complex, NaturalPos
from proveit.physics.quantum import Qmult, QmultCodomain

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([m, n], Conditional(Forall(instance_param_or_params = [M], instance_expr = InClass(Qmult(M), QmultCodomain), 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] \underset{{\scriptscriptstyle c}}{\in} \mathcal{Q^*}\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	32, 33
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: 30 body: 13
11	Operation	operator: 21 operands: 14
12	Operation	operator: 21 operands: 15
13	Conditional	value: 16 condition: 17
14	ExprTuple	32, 18
15	ExprTuple	33, 18
16	Operation	operator: 19 operands: 20
17	Operation	operator: 21 operands: 22
18	Literal
19	Literal
20	ExprTuple	23, 24
21	Literal
22	ExprTuple	30, 25
23	Operation	operator: 26 operand: 30
24	Literal
25	Operation	operator: 28 operands: 29
26	Literal
27	ExprTuple	30
28	Literal
29	NamedExprs	field: 31 rows: 32 columns: 33
30	Variable
31	Literal
32	Variable
33	Variable