Expression of type Lambda

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

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

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 1 body: 2
1	ExprTuple	21, 22
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9, 10
7	Literal
8	ExprTuple	11, 12
9	Operation	operator: 13 operands: 14
10	Operation	operator: 15 operand: 20
11	Operation	operator: 18 operands: 17
12	Operation	operator: 18 operands: 19
13	Literal
14	NamedExprs	field: 20 rows: 21 columns: 22
15	Literal
16	ExprTuple	20
17	ExprTuple	21, 23
18	Literal
19	ExprTuple	22, 23
20	Literal
21	Variable
22	Variable
23	Literal