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, c, i, j
from proveit.core_expr_types import a_1_to_i, c_1_to_j
from proveit.logic import And, Equals, InSet
from proveit.numbers import Complex, Mult, Neg, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = ExprTuple(Lambda([a_1_to_i, b, c_1_to_j], Conditional(Equals(Mult(a_1_to_i, Neg(b), c_1_to_j), Neg(Mult(a_1_to_i, b, c_1_to_j))), And(ExprRange(sub_expr1, InSet(IndexedVar(a, sub_expr1), Complex), one, i), InSet(b, Complex), ExprRange(sub_expr1, InSet(IndexedVar(c, 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}, b, c_{1}, c_{2}, \ldots, c_{j}\right) \mapsto \left\{\left(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{i} \cdot \left(-b\right)\cdot c_{1} \cdot  c_{2} \cdot  \ldots \cdot  c_{j}\right) = \left(-\left(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{i} \cdot b\cdot c_{1} \cdot  c_{2} \cdot  \ldots \cdot  c_{j}\right)\right) \textrm{ if } \left(a_{1} \in \mathbb{C}\right) ,  \left(a_{2} \in \mathbb{C}\right) ,  \ldots ,  \left(a_{i} \in \mathbb{C}\right) ,  b \in \mathbb{C}, \left(c_{1} \in \mathbb{C}\right) ,  \left(c_{2} \in \mathbb{C}\right) ,  \ldots ,  \left(c_{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: 26 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9, 10
7	Literal
8	ExprTuple	11, 12, 13
9	Operation	operator: 25 operands: 14
10	Operation	operator: 23 operand: 20
11	ExprRange	lambda_map: 16 start_index: 37 end_index: 35
12	Operation	operator: 28 operands: 17
13	ExprRange	lambda_map: 18 start_index: 37 end_index: 38
14	ExprTuple	30, 19, 32
15	ExprTuple	20
16	Lambda	parameter: 44 body: 21
17	ExprTuple	31, 33
18	Lambda	parameter: 44 body: 22
19	Operation	operator: 23 operand: 31
20	Operation	operator: 25 operands: 26
21	Operation	operator: 28 operands: 27
22	Operation	operator: 28 operands: 29
23	Literal
24	ExprTuple	31
25	Literal
26	ExprTuple	30, 31, 32
27	ExprTuple	39, 33
28	Literal
29	ExprTuple	40, 33
30	ExprRange	lambda_map: 34 start_index: 37 end_index: 35
31	Variable
32	ExprRange	lambda_map: 36 start_index: 37 end_index: 38
33	Literal
34	Lambda	parameter: 44 body: 39
35	Variable
36	Lambda	parameter: 44 body: 40
37	Literal
38	Variable
39	IndexedVar	variable: 41 index: 44
40	IndexedVar	variable: 42 index: 44
41	Variable
42	Variable
43	ExprTuple	44
44	Variable