# 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, Conditional, m
from proveit.core_expr_types import A_1_to_m
from proveit.logic import Equals, Forall, InSet
from proveit.numbers import NaturalPos

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\{\forall_{A_{1}, A_{2}, \ldots, A_{m}, B}~\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) \textrm{ if } m \in \mathbb{N}^+\right..

In [5]:
stored_expr.style_options()

namedescriptiondefaultcurrent valuerelated methods
condition_delimiter'comma' or 'and'commacomma('with_comma_delimiter', 'with_conjunction_delimiter')
In [6]:
# display the expression information
stored_expr.expr_info()

core typesub-expressionsexpression
0Conditionalvalue: 1
condition: 2
1Operationoperator: 3
operand: 7
2Operationoperator: 5
operands: 6
3Literal
4ExprTuple7
5Literal
6ExprTuple23, 8
7Lambdaparameters: 14
body: 9
8Literal
9Operationoperator: 10
operands: 11
10Literal
11ExprTuple12, 13
12Operationoperator: 18
operands: 14
13Operationoperator: 18
operands: 15
14ExprTuple20, 17
15ExprTuple16, 17
16Operationoperator: 18
operands: 19
17Variable
18Literal
19ExprTuple20
20ExprRangelambda_map: 21
start_index: 22
end_index: 23
21Lambdaparameter: 27
body: 24
22Literal
23Variable
24IndexedVarvariable: 25
index: 27
25Variable
26ExprTuple27
27Variable