Expression of type ExprTuple

from the theory of proveit.linear_algebra.matrices

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, n
from proveit.linear_algebra import MatrixSpace, VecSpaces
from proveit.logic import And, InClass, InSet
from proveit.numbers import NaturalPos, Real

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([m, n], Conditional(InClass(MatrixSpace(field = Real, rows = m, columns = n), VecSpaces(Real)), 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\{\mathbb{R}^{m \times n} \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(\mathbb{R}\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	22, 23
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operands: 7
5	Operation	operator: 8 operands: 9
6	Literal
7	ExprTuple	10, 11
8	Literal
9	ExprTuple	12, 13
10	Operation	operator: 14 operands: 15
11	Operation	operator: 16 operand: 21
12	Operation	operator: 19 operands: 18
13	Operation	operator: 19 operands: 20
14	Literal
15	NamedExprs	field: 21 rows: 22 columns: 23
16	Literal
17	ExprTuple	21
18	ExprTuple	22, 24
19	Literal
20	ExprTuple	23, 24
21	Literal
22	Variable
23	Variable
24	Literal