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, ExprRange, ExprTuple, IndexedVar, Lambda, Variable, a, b, i, j, x, y
from proveit.core_expr_types import a_1_to_i, b_1_to_j
from proveit.logic import And, Equals, InSet
from proveit.numbers import Complex, Mult, one, subtract

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = ExprTuple(Lambda([a_1_to_i, x, y, b_1_to_j], Conditional(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), And(ExprRange(sub_expr1, InSet(IndexedVar(a, sub_expr1), Complex), one, i), InSet(x, Complex), InSet(y, Complex), ExprRange(sub_expr1, InSet(IndexedVar(b, sub_expr1), Complex), one, 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(\left(a_{1}, a_{2}, \ldots, a_{i}, x, y, b_{1}, b_{2}, \ldots, b_{j}\right) \mapsto \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} \textrm{ if } \left(a_{1} \in \mathbb{C}\right) ,  \left(a_{2} \in \mathbb{C}\right) ,  \ldots ,  \left(a_{i} \in \mathbb{C}\right) ,  x \in \mathbb{C} ,  y \in \mathbb{C}, \left(b_{1} \in \mathbb{C}\right) ,  \left(b_{2} \in \mathbb{C}\right) ,  \ldots ,  \left(b_{j} \in \mathbb{C}\right)\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, 35, 43, 44
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operands: 7
5	Operation	operator: 8 operands: 9
6	Literal
7	ExprTuple	10, 11
8	Literal
9	ExprTuple	12, 13, 14, 15
10	Operation	operator: 40 operands: 16
11	Operation	operator: 27 operands: 17
12	ExprRange	lambda_map: 18 start_index: 48 end_index: 46
13	Operation	operator: 32 operands: 19
14	Operation	operator: 32 operands: 20
15	ExprRange	lambda_map: 21 start_index: 48 end_index: 49
16	ExprTuple	42, 22, 44
17	ExprTuple	23, 24
18	Lambda	parameter: 55 body: 25
19	ExprTuple	35, 37
20	ExprTuple	43, 37
21	Lambda	parameter: 55 body: 26
22	Operation	operator: 27 operands: 28
23	Operation	operator: 40 operands: 29
24	Operation	operator: 38 operand: 36
25	Operation	operator: 32 operands: 31
26	Operation	operator: 32 operands: 33
27	Literal
28	ExprTuple	35, 34
29	ExprTuple	42, 35, 44
30	ExprTuple	36
31	ExprTuple	50, 37
32	Literal
33	ExprTuple	51, 37
34	Operation	operator: 38 operand: 43
35	Variable
36	Operation	operator: 40 operands: 41
37	Literal
38	Literal
39	ExprTuple	43
40	Literal
41	ExprTuple	42, 43, 44
42	ExprRange	lambda_map: 45 start_index: 48 end_index: 46
43	Variable
44	ExprRange	lambda_map: 47 start_index: 48 end_index: 49
45	Lambda	parameter: 55 body: 50
46	Variable
47	Lambda	parameter: 55 body: 51
48	Literal
49	Variable
50	IndexedVar	variable: 52 index: 55
51	IndexedVar	variable: 53 index: 55
52	Variable
53	Variable
54	ExprTuple	55
55	Variable