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, i, j
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

# 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], Conditional(Equals(Mult(a_1_to_i, one, b_1_to_j), Mult(a_1_to_i, b_1_to_j)), And(ExprRange(sub_expr1, InSet(IndexedVar(a, sub_expr1), Complex), one, i), 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(a_{1}, a_{2}, \ldots, a_{i}, b_{1}, b_{2}, \ldots, b_{j}\right) \mapsto \left\{\left(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{i} \cdot 1\cdot b_{1} \cdot  b_{2} \cdot  \ldots \cdot  b_{j}\right) = \left(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{i}\cdot b_{1} \cdot  b_{2} \cdot  \ldots \cdot  b_{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), \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()

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
8	Operation	operator: 13 operands: 12
9	Operation	operator: 13 operands: 14
10	ExprRange	lambda_map: 15 start_index: 24 end_index: 22
11	ExprRange	lambda_map: 16 start_index: 24 end_index: 25
12	ExprTuple	17, 24, 18
13	Literal
14	ExprTuple	17, 18
15	Lambda	parameter: 35 body: 19
16	Lambda	parameter: 35 body: 20
17	ExprRange	lambda_map: 21 start_index: 24 end_index: 22
18	ExprRange	lambda_map: 23 start_index: 24 end_index: 25
19	Operation	operator: 27 operands: 26
20	Operation	operator: 27 operands: 28
21	Lambda	parameter: 35 body: 29
22	Variable
23	Lambda	parameter: 35 body: 30
24	Literal
25	Variable
26	ExprTuple	29, 31
27	Literal
28	ExprTuple	30, 31
29	IndexedVar	variable: 32 index: 35
30	IndexedVar	variable: 33 index: 35
31	Literal
32	Variable
33	Variable
34	ExprTuple	35
35	Variable