Expression of type Lambda

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, 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 = Lambda([a_1_to_i, b, c_1_to_j], Conditional(Equals(Neg(Mult(a_1_to_i, Neg(b), c_1_to_j)), 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(a_{1}, a_{2}, \ldots, a_{i}, b, c_{1}, c_{2}, \ldots, c_{j}\right) \mapsto \left\{\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)\right) = \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) \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..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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