Expression of type Lambda

from the theory of proveit.linear_algebra.addition

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, ExprRange, IndexedVar, Lambda, V, Variable, a, b, c, i, j, k
from proveit.core_expr_types import a_1_to_i, b_1_to_j, c_1_to_k
from proveit.linear_algebra import VecAdd
from proveit.logic import And, Equals, InSet
from proveit.numbers import one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Lambda([a_1_to_i, b_1_to_j, c_1_to_k], Conditional(Equals(VecAdd(a_1_to_i, b_1_to_j, c_1_to_k), VecAdd(a_1_to_i, VecAdd(b_1_to_j), c_1_to_k)).with_wrapping_at(2), And(ExprRange(sub_expr1, InSet(IndexedVar(a, sub_expr1), V), one, i), ExprRange(sub_expr1, InSet(IndexedVar(b, sub_expr1), V), one, j), ExprRange(sub_expr1, InSet(IndexedVar(c, sub_expr1), V), one, k))))

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_{i}, b_{1}, b_{2}, \ldots, b_{j}, c_{1}, c_{2}, \ldots, c_{k}\right) \mapsto \left\{\begin{array}{c} \begin{array}{l} \left(a_{1} +  a_{2} +  \ldots +  a_{i}+ b_{1} +  b_{2} +  \ldots +  b_{j}+ c_{1} +  c_{2} +  \ldots +  c_{k}\right) =  \\ \left(a_{1} +  a_{2} +  \ldots +  a_{i} + \left(b_{1} +  b_{2} +  \ldots +  b_{j}\right)+ c_{1} +  c_{2} +  \ldots +  c_{k}\right) \end{array} \end{array} \textrm{ if } \left(a_{1} \in V\right) ,  \left(a_{2} \in V\right) ,  \ldots ,  \left(a_{i} \in V\right), \left(b_{1} \in V\right) ,  \left(b_{2} \in V\right) ,  \ldots ,  \left(b_{j} \in V\right), \left(c_{1} \in V\right) ,  \left(c_{2} \in V\right) ,  \ldots ,  \left(c_{k} \in V\right)\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 13 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 4 operands: 5
3	Operation	operator: 6 operands: 7
4	Literal
5	ExprTuple	8, 9
6	Literal
7	ExprTuple	10, 11, 12
8	Operation	operator: 26 operands: 13
9	Operation	operator: 26 operands: 14
10	ExprRange	lambda_map: 15 start_index: 39 end_index: 25
11	ExprRange	lambda_map: 16 start_index: 39 end_index: 40
12	ExprRange	lambda_map: 17 start_index: 39 end_index: 29
13	ExprTuple	18, 34, 20
14	ExprTuple	18, 19, 20
15	Lambda	parameter: 46 body: 21
16	Lambda	parameter: 46 body: 22
17	Lambda	parameter: 46 body: 23
18	ExprRange	lambda_map: 24 start_index: 39 end_index: 25
19	Operation	operator: 26 operands: 27
20	ExprRange	lambda_map: 28 start_index: 39 end_index: 29
21	Operation	operator: 32 operands: 30
22	Operation	operator: 32 operands: 31
23	Operation	operator: 32 operands: 33
24	Lambda	parameter: 46 body: 35
25	Variable
26	Literal
27	ExprTuple	34
28	Lambda	parameter: 46 body: 36
29	Variable
30	ExprTuple	35, 37
31	ExprTuple	43, 37
32	Literal
33	ExprTuple	36, 37
34	ExprRange	lambda_map: 38 start_index: 39 end_index: 40
35	IndexedVar	variable: 41 index: 46
36	IndexedVar	variable: 42 index: 46
37	Variable
38	Lambda	parameter: 46 body: 43
39	Literal
40	Variable
41	Variable
42	Variable
43	IndexedVar	variable: 44 index: 46
44	Variable
45	ExprTuple	46
46	Variable