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, b, j
from proveit.core_expr_types import a_1_to_i, b_1_to_j, c_1_to_k
from proveit.logic import And, Equals, InSet
from proveit.numbers import Abs, Add, Complex, Mult, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_b", latex_format = r"{_{-}b}")
sub_expr2 = Variable("_a", latex_format = r"{_{-}a}")
expr = Lambda([b_1_to_j], Conditional(Equals(Mult(a_1_to_i, Abs(Add(b_1_to_j)), c_1_to_k), Abs(Add(ExprRange(sub_expr1, Mult(a_1_to_i, IndexedVar(b, sub_expr1), c_1_to_k), one, j)))).with_wrapping_at(2), And(ExprRange(sub_expr2, InSet(IndexedVar(b, sub_expr2), 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(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|b_{1} +  b_{2} +  \ldots +  b_{j}\right|\cdot c_{1} \cdot  c_{2} \cdot  \ldots \cdot  c_{k}\right) =  \\ \left|\left(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{i} \cdot b_{1}\cdot c_{1} \cdot  c_{2} \cdot  \ldots \cdot  c_{k}\right) +  \left(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{i} \cdot b_{2}\cdot c_{1} \cdot  c_{2} \cdot  \ldots \cdot  c_{k}\right) +  \ldots +  \left(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{i} \cdot b_{j}\cdot c_{1} \cdot  c_{2} \cdot  \ldots \cdot  c_{k}\right)\right| \end{array} \end{array} \textrm{ if } \left(b_{1} \in \mathbb{C}\right) \land  \left(b_{2} \in \mathbb{C}\right) \land  \ldots \land  \left(b_{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: 26 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
8	Operation	operator: 32 operands: 11
9	Operation	operator: 17 operand: 15
10	ExprRange	lambda_map: 13 start_index: 43 end_index: 31
11	ExprTuple	35, 14, 37
12	ExprTuple	15
13	Lambda	parameter: 51 body: 16
14	Operation	operator: 17 operand: 22
15	Operation	operator: 25 operands: 19
16	Operation	operator: 20 operands: 21
17	Literal
18	ExprTuple	22
19	ExprTuple	23
20	Literal
21	ExprTuple	34, 24
22	Operation	operator: 25 operands: 26
23	ExprRange	lambda_map: 27 start_index: 43 end_index: 31
24	Literal
25	Literal
26	ExprTuple	28
27	Lambda	parameter: 46 body: 29
28	ExprRange	lambda_map: 30 start_index: 43 end_index: 31
29	Operation	operator: 32 operands: 33
30	Lambda	parameter: 51 body: 34
31	Variable
32	Literal
33	ExprTuple	35, 36, 37
34	IndexedVar	variable: 40 index: 51
35	ExprRange	lambda_map: 38 start_index: 43 end_index: 39
36	IndexedVar	variable: 40 index: 46
37	ExprRange	lambda_map: 42 start_index: 43 end_index: 44
38	Lambda	parameter: 51 body: 45
39	Variable
40	Variable
41	ExprTuple	46
42	Lambda	parameter: 51 body: 47
43	Literal
44	Variable
45	IndexedVar	variable: 48 index: 51
46	Variable
47	IndexedVar	variable: 49 index: 51
48	Variable
49	Variable
50	ExprTuple	51
51	Variable