Expression of type Conditional

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, IndexedVar, 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 = 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\{\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..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

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