Expression of type ExprTuple

from the theory of proveit.numbers.multiplication

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, ExprTuple, Lambda, i, j, x, y
from proveit.core_expr_types import a_1_to_i, b_1_to_j
from proveit.logic import And, Equals, Forall, InSet
from proveit.numbers import Complex, Mult, Natural, subtract

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([i, j], Conditional(Forall(instance_param_or_params = [a_1_to_i, x, y, b_1_to_j], instance_expr = Equals(Mult(a_1_to_i, subtract(x, y), b_1_to_j), subtract(Mult(a_1_to_i, x, b_1_to_j), Mult(a_1_to_i, y, b_1_to_j))).with_wrapping_at(2), domain = Complex), And(InSet(i, Natural), InSet(j, Natural)))))

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(i, j\right) \mapsto \left\{\forall_{a_{1}, a_{2}, \ldots, a_{i}, x, y, b_{1}, b_{2}, \ldots, b_{j} \in \mathbb{C}}~\left(\begin{array}{c} \begin{array}{l} \left(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{i} \cdot \left(x - y\right)\cdot b_{1} \cdot  b_{2} \cdot  \ldots \cdot  b_{j}\right) =  \\ \left(\left(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{i} \cdot x\cdot b_{1} \cdot  b_{2} \cdot  \ldots \cdot  b_{j}\right) - \left(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{i} \cdot y\cdot b_{1} \cdot  b_{2} \cdot  \ldots \cdot  b_{j}\right)\right) \end{array} \end{array}\right) \textrm{ if } i \in \mathbb{N} ,  j \in \mathbb{N}\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	59, 62
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 9
5	Operation	operator: 21 operands: 8
6	Literal
7	ExprTuple	9
8	ExprTuple	10, 11
9	Lambda	parameters: 12 body: 13
10	Operation	operator: 45 operands: 14
11	Operation	operator: 45 operands: 15
12	ExprTuple	55, 48, 56, 57
13	Conditional	value: 16 condition: 17
14	ExprTuple	59, 18
15	ExprTuple	62, 18
16	Operation	operator: 19 operands: 20
17	Operation	operator: 21 operands: 22
18	Literal
19	Literal
20	ExprTuple	23, 24
21	Literal
22	ExprTuple	25, 26, 27, 28
23	Operation	operator: 53 operands: 29
24	Operation	operator: 40 operands: 30
25	ExprRange	lambda_map: 31 start_index: 61 end_index: 59
26	Operation	operator: 45 operands: 32
27	Operation	operator: 45 operands: 33
28	ExprRange	lambda_map: 34 start_index: 61 end_index: 62
29	ExprTuple	55, 35, 57
30	ExprTuple	36, 37
31	Lambda	parameter: 68 body: 38
32	ExprTuple	48, 50
33	ExprTuple	56, 50
34	Lambda	parameter: 68 body: 39
35	Operation	operator: 40 operands: 41
36	Operation	operator: 53 operands: 42
37	Operation	operator: 51 operand: 49
38	Operation	operator: 45 operands: 44
39	Operation	operator: 45 operands: 46
40	Literal
41	ExprTuple	48, 47
42	ExprTuple	55, 48, 57
43	ExprTuple	49
44	ExprTuple	63, 50
45	Literal
46	ExprTuple	64, 50
47	Operation	operator: 51 operand: 56
48	Variable
49	Operation	operator: 53 operands: 54
50	Literal
51	Literal
52	ExprTuple	56
53	Literal
54	ExprTuple	55, 56, 57
55	ExprRange	lambda_map: 58 start_index: 61 end_index: 59
56	Variable
57	ExprRange	lambda_map: 60 start_index: 61 end_index: 62
58	Lambda	parameter: 68 body: 63
59	Variable
60	Lambda	parameter: 68 body: 64
61	Literal
62	Variable
63	IndexedVar	variable: 65 index: 68
64	IndexedVar	variable: 66 index: 68
65	Variable
66	Variable
67	ExprTuple	68
68	Variable