Expression of type Conditional

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, i, j
from proveit.core_expr_types import a_1_to_i, b_1_to_j
from proveit.logic import And, Equals, Forall, InSet
from proveit.numbers import Complex, Mult, Natural, zero

# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [a_1_to_i, b_1_to_j], instance_expr = Equals(Mult(a_1_to_i, zero, b_1_to_j), zero), 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\{\forall_{a_{1}, a_{2}, \ldots, a_{i}, b_{1}, b_{2}, \ldots, b_{j} \in \mathbb{C}}~\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\right) \textrm{ if } i \in \mathbb{N} ,  j \in \mathbb{N}\right..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Conditional	value: 1 condition: 2
1	Operation	operator: 3 operand: 6
2	Operation	operator: 18 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	7, 8
6	Lambda	parameters: 9 body: 10
7	Operation	operator: 38 operands: 11
8	Operation	operator: 38 operands: 12
9	ExprTuple	27, 29
10	Conditional	value: 13 condition: 14
11	ExprTuple	33, 15
12	ExprTuple	36, 15
13	Operation	operator: 16 operands: 17
14	Operation	operator: 18 operands: 19
15	Literal
16	Literal
17	ExprTuple	20, 28
18	Literal
19	ExprTuple	21, 22
20	Operation	operator: 23 operands: 24
21	ExprRange	lambda_map: 25 start_index: 35 end_index: 33
22	ExprRange	lambda_map: 26 start_index: 35 end_index: 36
23	Literal
24	ExprTuple	27, 28, 29
25	Lambda	parameter: 46 body: 30
26	Lambda	parameter: 46 body: 31
27	ExprRange	lambda_map: 32 start_index: 35 end_index: 33
28	Literal
29	ExprRange	lambda_map: 34 start_index: 35 end_index: 36
30	Operation	operator: 38 operands: 37
31	Operation	operator: 38 operands: 39
32	Lambda	parameter: 46 body: 40
33	Variable
34	Lambda	parameter: 46 body: 41
35	Literal
36	Variable
37	ExprTuple	40, 42
38	Literal
39	ExprTuple	41, 42
40	IndexedVar	variable: 43 index: 46
41	IndexedVar	variable: 44 index: 46
42	Literal
43	Variable
44	Variable
45	ExprTuple	46
46	Variable