Expression of type Conditional

from the theory of proveit.numbers.addition

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, b, i, j
from proveit.core_expr_types import a_1_to_i, c_1_to_j
from proveit.logic import And, Forall, InSet
from proveit.numbers import Add, Less, Natural, RationalNeg, RationalNonPos, zero

# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [a_1_to_i, b, c_1_to_j], instance_expr = InSet(Add(a_1_to_i, b, c_1_to_j), RationalNeg), domain = RationalNonPos, condition = Less(b, zero)), 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, c_{1}, c_{2}, \ldots, c_{j} \in \mathbb{Q}^{\leq 0}~|~b < 0}~\left(\left(a_{1} +  a_{2} +  \ldots +  a_{i} + b+ c_{1} +  c_{2} +  \ldots +  c_{j}\right) \in \mathbb{Q}^-\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: 16 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	7, 8
6	Lambda	parameters: 25 body: 9
7	Operation	operator: 43 operands: 10
8	Operation	operator: 43 operands: 11
9	Conditional	value: 12 condition: 13
10	ExprTuple	38, 14
11	ExprTuple	41, 14
12	Operation	operator: 43 operands: 15
13	Operation	operator: 16 operands: 17
14	Literal
15	ExprTuple	18, 19
16	Literal
17	ExprTuple	20, 21, 22, 23
18	Operation	operator: 24 operands: 25
19	Literal
20	ExprRange	lambda_map: 26 start_index: 40 end_index: 38
21	Operation	operator: 43 operands: 27
22	ExprRange	lambda_map: 28 start_index: 40 end_index: 41
23	Operation	operator: 29 operands: 30
24	Literal
25	ExprTuple	31, 35, 32
26	Lambda	parameter: 51 body: 33
27	ExprTuple	35, 47
28	Lambda	parameter: 51 body: 34
29	Literal
30	ExprTuple	35, 36
31	ExprRange	lambda_map: 37 start_index: 40 end_index: 38
32	ExprRange	lambda_map: 39 start_index: 40 end_index: 41
33	Operation	operator: 43 operands: 42
34	Operation	operator: 43 operands: 44
35	Variable
36	Literal
37	Lambda	parameter: 51 body: 45
38	Variable
39	Lambda	parameter: 51 body: 46
40	Literal
41	Variable
42	ExprTuple	45, 47
43	Literal
44	ExprTuple	46, 47
45	IndexedVar	variable: 48 index: 51
46	IndexedVar	variable: 49 index: 51
47	Literal
48	Variable
49	Variable
50	ExprTuple	51
51	Variable