Expression of type Lambda

from the theory of proveit.linear_algebra

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 B, Lambda
from proveit.core_expr_types import A_1_to_m
from proveit.linear_algebra import LinMapAdd
from proveit.logic import Equals

# build up the expression from sub-expressions
expr = Lambda([A_1_to_m, B], Equals(LinMapAdd(A_1_to_m, B), LinMapAdd(LinMapAdd(A_1_to_m), B)).with_wrapping_at(2))

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(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)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 6 body: 1
1	Operation	operator: 2 operands: 3
2	Literal
3	ExprTuple	4, 5
4	Operation	operator: 10 operands: 6
5	Operation	operator: 10 operands: 7
6	ExprTuple	12, 9
7	ExprTuple	8, 9
8	Operation	operator: 10 operands: 11
9	Variable
10	Literal
11	ExprTuple	12
12	ExprRange	lambda_map: 13 start_index: 14 end_index: 15
13	Lambda	parameter: 19 body: 16
14	Literal
15	Variable
16	IndexedVar	variable: 17 index: 19
17	Variable
18	ExprTuple	19
19	Variable