Expression of type Conditional

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

# build up the expression from sub-expressions
expr = Conditional(InClass(MatrixSpace(field = Rational, rows = m, columns = n), VecSpaces(Rational)), 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\{\mathbb{Q}^{m \times n} \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(\mathbb{Q}\right) \textrm{ if } m \in \mathbb{N}^+ ,  n \in \mathbb{N}^+\right..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Conditional	value: 1 condition: 2
1	Operation	operator: 3 operands: 4
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7, 8
5	Literal
6	ExprTuple	9, 10
7	Operation	operator: 11 operands: 12
8	Operation	operator: 13 operand: 18
9	Operation	operator: 16 operands: 15
10	Operation	operator: 16 operands: 17
11	Literal
12	NamedExprs	field: 18 rows: 19 columns: 20
13	Literal
14	ExprTuple	18
15	ExprTuple	19, 21
16	Literal
17	ExprTuple	20, 21
18	Literal
19	Variable
20	Variable
21	Literal