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, ExprTuple, Lambda, b, i, j
from proveit.core_expr_types import a_1_to_i, c_1_to_j
from proveit.logic import And, Equals, Forall, InSet
from proveit.numbers import Complex, Mult, Natural, Neg

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([i, j], Conditional(Forall(instance_param_or_params = [a_1_to_i, b, c_1_to_j], instance_expr = Equals(Neg(Mult(a_1_to_i, Neg(b), c_1_to_j)), Mult(a_1_to_i, b, c_1_to_j)), domain = Complex), And(InSet(i, Natural), InSet(j, Natural)))))

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(i, j\right) \mapsto \left\{\forall_{a_{1}, a_{2}, \ldots, a_{i}, b, c_{1}, c_{2}, \ldots, c_{j} \in \mathbb{C}}~\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)\right) \textrm{ if } i \in \mathbb{N} ,  j \in \mathbb{N}\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	45, 50
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 9
5	Operation	operator: 20 operands: 8
6	Literal
7	ExprTuple	9
8	ExprTuple	10, 11
9	Lambda	parameters: 28 body: 12
10	Operation	operator: 38 operands: 13
11	Operation	operator: 38 operands: 14
12	Conditional	value: 15 condition: 16
13	ExprTuple	45, 17
14	ExprTuple	50, 17
15	Operation	operator: 18 operands: 19
16	Operation	operator: 20 operands: 21
17	Literal
18	Literal
19	ExprTuple	22, 23
20	Literal
21	ExprTuple	24, 25, 26
22	Operation	operator: 46 operand: 32
23	Operation	operator: 35 operands: 28
24	ExprRange	lambda_map: 29 start_index: 49 end_index: 45
25	Operation	operator: 38 operands: 30
26	ExprRange	lambda_map: 31 start_index: 49 end_index: 50
27	ExprTuple	32
28	ExprTuple	40, 52, 42
29	Lambda	parameter: 57 body: 33
30	ExprTuple	52, 43
31	Lambda	parameter: 57 body: 34
32	Operation	operator: 35 operands: 36
33	Operation	operator: 38 operands: 37
34	Operation	operator: 38 operands: 39
35	Literal
36	ExprTuple	40, 41, 42
37	ExprTuple	51, 43
38	Literal
39	ExprTuple	53, 43
40	ExprRange	lambda_map: 44 start_index: 49 end_index: 45
41	Operation	operator: 46 operand: 52
42	ExprRange	lambda_map: 48 start_index: 49 end_index: 50
43	Literal
44	Lambda	parameter: 57 body: 51
45	Variable
46	Literal
47	ExprTuple	52
48	Lambda	parameter: 57 body: 53
49	Literal
50	Variable
51	IndexedVar	variable: 54 index: 57
52	Variable
53	IndexedVar	variable: 55 index: 57
54	Variable
55	Variable
56	ExprTuple	57
57	Variable