# from the theory of proveit.linear_algebra¶

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.
# import Expression classes needed to build the expression
from proveit import B, Lambda
from proveit.core_expr_types import A_1_to_m
from proveit.logic import Equals

In [2]:
# build up the expression from sub-expressions

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(A_{1}, A_{2}, \ldots, A_{m}, B\right) \mapsto \left(\begin{array}{c} \begin{array}{l} \left(A_{1} +  A_{2} +  \ldots +  A_{m} + B\right) =  \\ \left(\left(A_{1} +  A_{2} +  \ldots +  A_{m}\right) + B\right) \end{array} \end{array}\right)

In [5]:
stored_expr.style_options()

no style options
In [6]:
# display the expression information
stored_expr.expr_info()

core typesub-expressionsexpression
0Lambdaparameters: 6
body: 1
1Operationoperator: 2
operands: 3
2Literal
3ExprTuple4, 5
4Operationoperator: 10
operands: 6
5Operationoperator: 10
operands: 7
6ExprTuple12, 9
7ExprTuple8, 9
8Operationoperator: 10
operands: 11
9Variable
10Literal
11ExprTuple12
12ExprRangelambda_map: 13
start_index: 14
end_index: 15
13Lambdaparameter: 19
body: 16
14Literal
15Variable
16IndexedVarvariable: 17
index: 19
17Variable
18ExprTuple19
19Variable