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, Function, Lambda, V, s
from proveit.core_expr_types import Q__b_1_to_j, a_1_to_i, b_1_to_j, c_1_to_k, f__b_1_to_j
from proveit.linear_algebra import ScalarMult, TensorProd
from proveit.logic import InSet

# build up the expression from sub-expressions
sub_expr1 = [b_1_to_j]
expr = Lambda(sub_expr1, Conditional(InSet(TensorProd(a_1_to_i, ScalarMult(Function(s, sub_expr1), f__b_1_to_j), c_1_to_k), V), Q__b_1_to_j))

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(b_{1}, b_{2}, \ldots, b_{j}\right) \mapsto \left\{\left(a_{1} {\otimes}  a_{2} {\otimes}  \ldots {\otimes}  a_{i} {\otimes} \left(s\left(b_{1}, b_{2}, \ldots, b_{j}\right) \cdot f\left(b_{1}, b_{2}, \ldots, b_{j}\right)\right){\otimes} c_{1} {\otimes}  c_{2} {\otimes}  \ldots {\otimes}  c_{k}\right) \in V \textrm{ if } Q\left(b_{1}, b_{2}, \ldots, b_{j}\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: 27 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 4 operands: 5
3	Operation	operator: 6 operands: 27
4	Literal
5	ExprTuple	7, 8
6	Variable
7	Operation	operator: 9 operands: 10
8	Variable
9	Literal
10	ExprTuple	11, 12, 13
11	ExprRange	lambda_map: 14 start_index: 31 end_index: 15
12	Operation	operator: 16 operands: 17
13	ExprRange	lambda_map: 18 start_index: 31 end_index: 19
14	Lambda	parameter: 36 body: 20
15	Variable
16	Literal
17	ExprTuple	21, 22
18	Lambda	parameter: 36 body: 23
19	Variable
20	IndexedVar	variable: 24 index: 36
21	Operation	operator: 25 operands: 27
22	Operation	operator: 26 operands: 27
23	IndexedVar	variable: 28 index: 36
24	Variable
25	Variable
26	Variable
27	ExprTuple	29
28	Variable
29	ExprRange	lambda_map: 30 start_index: 31 end_index: 32
30	Lambda	parameter: 36 body: 33
31	Literal
32	Variable
33	IndexedVar	variable: 34 index: 36
34	Variable
35	ExprTuple	36
36	Variable