# 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, Lambda, 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())

m \mapsto \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()

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

core typesub-expressionsexpression
0Lambdaparameter: 25
body: 2
1ExprTuple25
2Conditionalvalue: 3
condition: 4
3Operationoperator: 5
operand: 9
4Operationoperator: 7
operands: 8
5Literal
6ExprTuple9
7Literal
8ExprTuple25, 10
9Lambdaparameters: 16
body: 11
10Literal
11Operationoperator: 12
operands: 13
12Literal
13ExprTuple14, 15
14Operationoperator: 20
operands: 16
15Operationoperator: 20
operands: 17
16ExprTuple22, 19
17ExprTuple18, 19
18Operationoperator: 20
operands: 21
19Variable
20Literal
21ExprTuple22
22ExprRangelambda_map: 23
start_index: 24
end_index: 25
23Lambdaparameter: 29
body: 26
24Literal
25Variable
26IndexedVarvariable: 27
index: 29
27Variable
28ExprTuple29
29Variable