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Expression of type Lambda

from the theory of proveit.linear_algebra.matrices

In [1]:
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
In [2]:
# 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:
In [3]:
# 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
In [4]:
# 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..
In [5]:
stored_expr.style_options()
no style options
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Lambdaparameters: 1
body: 2
1ExprTuple21, 22
2Conditionalvalue: 3
condition: 4
3Operationoperator: 5
operands: 6
4Operationoperator: 7
operands: 8
5Literal
6ExprTuple9, 10
7Literal
8ExprTuple11, 12
9Operationoperator: 13
operands: 14
10Operationoperator: 15
operand: 20
11Operationoperator: 18
operands: 17
12Operationoperator: 18
operands: 19
13Literal
14NamedExprsfield: 20
rows: 21
columns: 22
15Literal
16ExprTuple20
17ExprTuple21, 23
18Literal
19ExprTuple22, 23
20Literal
21Variable
22Variable
23Literal