Expression of type ExprTuple

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 ExprTuple, 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, VecSum
from proveit.logic import Equals, Forall, Implies, InSet

# build up the expression from sub-expressions
sub_expr1 = [b_1_to_j]
sub_expr2 = Function(s, sub_expr1)
sub_expr3 = ScalarMult(sub_expr2, f__b_1_to_j)
expr = ExprTuple(Lambda([a_1_to_i, c_1_to_k], Implies(Forall(instance_param_or_params = sub_expr1, instance_expr = InSet(TensorProd(a_1_to_i, sub_expr3, c_1_to_k), V), condition = Q__b_1_to_j), Equals(TensorProd(a_1_to_i, VecSum(index_or_indices = sub_expr1, summand = sub_expr3, condition = Q__b_1_to_j), c_1_to_k), VecSum(index_or_indices = sub_expr1, summand = ScalarMult(sub_expr2, TensorProd(a_1_to_i, f__b_1_to_j, c_1_to_k)), condition = Q__b_1_to_j)).with_wrapping_at(1)).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(\left(a_{1}, a_{2}, \ldots, a_{i}, c_{1}, c_{2}, \ldots, c_{k}\right) \mapsto \left(\begin{array}{c} \begin{array}{l} \left[\forall_{b_{1}, b_{2}, \ldots, b_{j}~|~Q\left(b_{1}, b_{2}, \ldots, b_{j}\right)}~\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\right)\right] \Rightarrow  \\ \left(\begin{array}{c} \begin{array}{l} \left(a_{1} {\otimes}  a_{2} {\otimes}  \ldots {\otimes}  a_{i} {\otimes} \left[\sum_{b_{1}, b_{2}, \ldots, b_{j}~|~Q\left(b_{1}, b_{2}, \ldots, b_{j}\right)}~\left(s\left(b_{1}, b_{2}, \ldots, b_{j}\right) \cdot f\left(b_{1}, b_{2}, \ldots, b_{j}\right)\right)\right]{\otimes} c_{1} {\otimes}  c_{2} {\otimes}  \ldots {\otimes}  c_{k}\right) \\  = \left[\sum_{b_{1}, b_{2}, \ldots, b_{j}~|~Q\left(b_{1}, b_{2}, \ldots, b_{j}\right)}~\left(s\left(b_{1}, b_{2}, \ldots, b_{j}\right) \cdot \left(a_{1} {\otimes}  a_{2} {\otimes}  \ldots {\otimes}  a_{i} {\otimes} f\left(b_{1}, b_{2}, \ldots, b_{j}\right){\otimes} c_{1} {\otimes}  c_{2} {\otimes}  \ldots {\otimes}  c_{k}\right)\right)\right] \end{array} \end{array}\right) \end{array} \end{array}\right)\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameters: 2 body: 3
2	ExprTuple	42, 44
3	Operation	operator: 4 operands: 5
4	Literal
5	ExprTuple	6, 7
6	Operation	operator: 8 operand: 12
7	Operation	operator: 10 operands: 11
8	Literal
9	ExprTuple	12
10	Literal
11	ExprTuple	13, 14
12	Lambda	parameters: 49 body: 15
13	Operation	operator: 39 operands: 16
14	Operation	operator: 23 operand: 20
15	Conditional	value: 18 condition: 34
16	ExprTuple	42, 19, 44
17	ExprTuple	20
18	Operation	operator: 21 operands: 22
19	Operation	operator: 23 operand: 28
20	Lambda	parameters: 49 body: 25
21	Literal
22	ExprTuple	26, 27
23	Literal
24	ExprTuple	28
25	Conditional	value: 29 condition: 34
26	Operation	operator: 39 operands: 30
27	Variable
28	Lambda	parameters: 49 body: 31
29	Operation	operator: 36 operands: 32
30	ExprTuple	42, 33, 44
31	Conditional	value: 33 condition: 34
32	ExprTuple	41, 35
33	Operation	operator: 36 operands: 37
34	Operation	operator: 38 operands: 49
35	Operation	operator: 39 operands: 40
36	Literal
37	ExprTuple	41, 43
38	Variable
39	Literal
40	ExprTuple	42, 43, 44
41	Operation	operator: 45 operands: 49
42	ExprRange	lambda_map: 46 start_index: 57 end_index: 47
43	Operation	operator: 48 operands: 49
44	ExprRange	lambda_map: 50 start_index: 57 end_index: 51
45	Variable
46	Lambda	parameter: 63 body: 52
47	Variable
48	Variable
49	ExprTuple	53
50	Lambda	parameter: 63 body: 54
51	Variable
52	IndexedVar	variable: 55 index: 63
53	ExprRange	lambda_map: 56 start_index: 57 end_index: 58
54	IndexedVar	variable: 59 index: 63
55	Variable
56	Lambda	parameter: 63 body: 60
57	Literal
58	Variable
59	Variable
60	IndexedVar	variable: 61 index: 63
61	Variable
62	ExprTuple	63
63	Variable