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, d, i, j, k
from proveit.core_expr_types import a_1_to_i, b_1_to_j, d_1_to_k
from proveit.logic import And, Equals, InSet
from proveit.numbers import Complex, Mult, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Lambda([a_1_to_i, b_1_to_j, c, d_1_to_k], Conditional(Equals(Mult(a_1_to_i, b_1_to_j, c, d_1_to_k), Mult(a_1_to_i, c, b_1_to_j, d_1_to_k)).with_wrapping_at(2), And(ExprRange(sub_expr1, InSet(IndexedVar(a, sub_expr1), Complex), one, i), ExprRange(sub_expr1, InSet(IndexedVar(b, sub_expr1), Complex), one, j), InSet(c, Complex), ExprRange(sub_expr1, InSet(IndexedVar(d, sub_expr1), Complex), one, k))))

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_{1}, b_{2}, \ldots, b_{j}, c, d_{1}, d_{2}, \ldots, d_{k}\right) \mapsto \left\{\begin{array}{c} \begin{array}{l} \left(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{i}\cdot b_{1} \cdot  b_{2} \cdot  \ldots \cdot  b_{j} \cdot c\cdot d_{1} \cdot  d_{2} \cdot  \ldots \cdot  d_{k}\right) =  \\ \left(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{i} \cdot c\cdot b_{1} \cdot  b_{2} \cdot  \ldots \cdot  b_{j}\cdot d_{1} \cdot  d_{2} \cdot  \ldots \cdot  d_{k}\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), \left(b_{1} \in \mathbb{C}\right) ,  \left(b_{2} \in \mathbb{C}\right) ,  \ldots ,  \left(b_{j} \in \mathbb{C}\right) ,  c \in \mathbb{C}, \left(d_{1} \in \mathbb{C}\right) ,  \left(d_{2} \in \mathbb{C}\right) ,  \ldots ,  \left(d_{k} \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, 13
8	Operation	operator: 15 operands: 14
9	Operation	operator: 15 operands: 16
10	ExprRange	lambda_map: 17 start_index: 33 end_index: 29
11	ExprRange	lambda_map: 18 start_index: 33 end_index: 31
12	Operation	operator: 37 operands: 19
13	ExprRange	lambda_map: 20 start_index: 33 end_index: 34
14	ExprTuple	21, 22, 26, 23
15	Literal
16	ExprTuple	21, 26, 22, 23
17	Lambda	parameter: 47 body: 24
18	Lambda	parameter: 47 body: 25
19	ExprTuple	26, 42
20	Lambda	parameter: 47 body: 27
21	ExprRange	lambda_map: 28 start_index: 33 end_index: 29
22	ExprRange	lambda_map: 30 start_index: 33 end_index: 31
23	ExprRange	lambda_map: 32 start_index: 33 end_index: 34
24	Operation	operator: 37 operands: 35
25	Operation	operator: 37 operands: 36
26	Variable
27	Operation	operator: 37 operands: 38
28	Lambda	parameter: 47 body: 39
29	Variable
30	Lambda	parameter: 47 body: 40
31	Variable
32	Lambda	parameter: 47 body: 41
33	Literal
34	Variable
35	ExprTuple	39, 42
36	ExprTuple	40, 42
37	Literal
38	ExprTuple	41, 42
39	IndexedVar	variable: 43 index: 47
40	IndexedVar	variable: 44 index: 47
41	IndexedVar	variable: 45 index: 47
42	Literal
43	Variable
44	Variable
45	Variable
46	ExprTuple	47
47	Variable