Expression of type Lambda

from the theory of proveit.linear_algebra.tensors

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, K, Lambda, V, Variable, b, j
from proveit.core_expr_types import a_1_to_i, b_1_to_j, c_1_to_k
from proveit.linear_algebra import TensorProd, VecAdd, VecSpaces
from proveit.logic import Equals, Forall, Implies, InClass, InSet
from proveit.numbers import one

# build up the expression from sub-expressions
sub_expr1 = Variable("_b", latex_format = r"{_{-}b}")
sub_expr2 = TensorProd(a_1_to_i, VecAdd(b_1_to_j), c_1_to_k)
expr = Lambda(V, Conditional(Forall(instance_param_or_params = [a_1_to_i, b_1_to_j, c_1_to_k], instance_expr = Implies(InSet(sub_expr2, V), Equals(sub_expr2, VecAdd(ExprRange(sub_expr1, TensorProd(a_1_to_i, IndexedVar(b, sub_expr1), c_1_to_k), one, j))).with_wrapping_at(2)).with_wrapping_at(2)).with_wrapping(), InClass(V, VecSpaces(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())

V \mapsto \left\{\begin{array}{l}\forall_{a_{1}, a_{2}, \ldots, a_{i}, b_{1}, b_{2}, \ldots, b_{j}, c_{1}, c_{2}, \ldots, c_{k}}~\\
\left(\begin{array}{c} \begin{array}{l} \left(\left(a_{1} {\otimes}  a_{2} {\otimes}  \ldots {\otimes}  a_{i} {\otimes} \left(b_{1} +  b_{2} +  \ldots +  b_{j}\right){\otimes} c_{1} {\otimes}  c_{2} {\otimes}  \ldots {\otimes}  c_{k}\right) \in V\right) \Rightarrow  \\ \left(\begin{array}{c} \begin{array}{l} \left(a_{1} {\otimes}  a_{2} {\otimes}  \ldots {\otimes}  a_{i} {\otimes} \left(b_{1} +  b_{2} +  \ldots +  b_{j}\right){\otimes} c_{1} {\otimes}  c_{2} {\otimes}  \ldots {\otimes}  c_{k}\right) =  \\ \left(\left(a_{1} {\otimes}  a_{2} {\otimes}  \ldots {\otimes}  a_{i} {\otimes} b_{1}{\otimes} c_{1} {\otimes}  c_{2} {\otimes}  \ldots {\otimes}  c_{k}\right) +  \left(a_{1} {\otimes}  a_{2} {\otimes}  \ldots {\otimes}  a_{i} {\otimes} b_{2}{\otimes} c_{1} {\otimes}  c_{2} {\otimes}  \ldots {\otimes}  c_{k}\right) +  \ldots +  \left(a_{1} {\otimes}  a_{2} {\otimes}  \ldots {\otimes}  a_{i} {\otimes} b_{j}{\otimes} c_{1} {\otimes}  c_{2} {\otimes}  \ldots {\otimes}  c_{k}\right)\right) \end{array} \end{array}\right) \end{array} \end{array}\right)\end{array} \textrm{ if } V \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 24 body: 2
1	ExprTuple	24
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 9
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9
7	Literal
8	ExprTuple	24, 10
9	Lambda	parameters: 11 body: 12
10	Operation	operator: 13 operand: 17
11	ExprTuple	41, 34, 43
12	Operation	operator: 15 operands: 16
13	Literal
14	ExprTuple	17
15	Literal
16	ExprTuple	18, 19
17	Variable
18	Operation	operator: 20 operands: 21
19	Operation	operator: 22 operands: 23
20	Literal
21	ExprTuple	25, 24
22	Literal
23	ExprTuple	25, 26
24	Variable
25	Operation	operator: 38 operands: 27
26	Operation	operator: 31 operands: 28
27	ExprTuple	41, 29, 43
28	ExprTuple	30
29	Operation	operator: 31 operands: 32
30	ExprRange	lambda_map: 33 start_index: 49 end_index: 37
31	Literal
32	ExprTuple	34
33	Lambda	parameter: 52 body: 35
34	ExprRange	lambda_map: 36 start_index: 49 end_index: 37
35	Operation	operator: 38 operands: 39
36	Lambda	parameter: 57 body: 40
37	Variable
38	Literal
39	ExprTuple	41, 42, 43
40	IndexedVar	variable: 46 index: 57
41	ExprRange	lambda_map: 44 start_index: 49 end_index: 45
42	IndexedVar	variable: 46 index: 52
43	ExprRange	lambda_map: 48 start_index: 49 end_index: 50
44	Lambda	parameter: 57 body: 51
45	Variable
46	Variable
47	ExprTuple	52
48	Lambda	parameter: 57 body: 53
49	Literal
50	Variable
51	IndexedVar	variable: 54 index: 57
52	Variable
53	IndexedVar	variable: 55 index: 57
54	Variable
55	Variable
56	ExprTuple	57
57	Variable