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, 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, zero

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = ExprTuple(Lambda([a_1_to_i, b_1_to_j], Conditional(Equals(Mult(a_1_to_i, zero, b_1_to_j), zero), 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(\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 0\cdot b_{1} \cdot  b_{2} \cdot  \ldots \cdot  b_{j}\right) = 0 \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..\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: 2 body: 3
2	ExprTuple	17, 19
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operands: 7
5	Operation	operator: 8 operands: 9
6	Literal
7	ExprTuple	10, 18
8	Literal
9	ExprTuple	11, 12
10	Operation	operator: 13 operands: 14
11	ExprRange	lambda_map: 15 start_index: 25 end_index: 23
12	ExprRange	lambda_map: 16 start_index: 25 end_index: 26
13	Literal
14	ExprTuple	17, 18, 19
15	Lambda	parameter: 36 body: 20
16	Lambda	parameter: 36 body: 21
17	ExprRange	lambda_map: 22 start_index: 25 end_index: 23
18	Literal
19	ExprRange	lambda_map: 24 start_index: 25 end_index: 26
20	Operation	operator: 28 operands: 27
21	Operation	operator: 28 operands: 29
22	Lambda	parameter: 36 body: 30
23	Variable
24	Lambda	parameter: 36 body: 31
25	Literal
26	Variable
27	ExprTuple	30, 32
28	Literal
29	ExprTuple	31, 32
30	IndexedVar	variable: 33 index: 36
31	IndexedVar	variable: 34 index: 36
32	Literal
33	Variable
34	Variable
35	ExprTuple	36
36	Variable