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, Natural, NaturalPos, greater, 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), NaturalPos), domain = Natural, condition = greater(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{N}~|~b > 0}~\left(\left(a_{1} +  a_{2} +  \ldots +  a_{i} + b+ c_{1} +  c_{2} +  \ldots +  c_{j}\right) \in \mathbb{N}^+\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: 15 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	7, 8
6	Lambda	parameters: 24 body: 9
7	Operation	operator: 42 operands: 10
8	Operation	operator: 42 operands: 11
9	Conditional	value: 12 condition: 13
10	ExprTuple	37, 46
11	ExprTuple	40, 46
12	Operation	operator: 42 operands: 14
13	Operation	operator: 15 operands: 16
14	ExprTuple	17, 18
15	Literal
16	ExprTuple	19, 20, 21, 22
17	Operation	operator: 23 operands: 24
18	Literal
19	ExprRange	lambda_map: 25 start_index: 39 end_index: 37
20	Operation	operator: 42 operands: 26
21	ExprRange	lambda_map: 27 start_index: 39 end_index: 40
22	Operation	operator: 28 operands: 29
23	Literal
24	ExprTuple	30, 35, 31
25	Lambda	parameter: 50 body: 32
26	ExprTuple	35, 46
27	Lambda	parameter: 50 body: 33
28	Literal
29	ExprTuple	34, 35
30	ExprRange	lambda_map: 36 start_index: 39 end_index: 37
31	ExprRange	lambda_map: 38 start_index: 39 end_index: 40
32	Operation	operator: 42 operands: 41
33	Operation	operator: 42 operands: 43
34	Literal
35	Variable
36	Lambda	parameter: 50 body: 44
37	Variable
38	Lambda	parameter: 50 body: 45
39	Literal
40	Variable
41	ExprTuple	44, 46
42	Literal
43	ExprTuple	45, 46
44	IndexedVar	variable: 47 index: 50
45	IndexedVar	variable: 48 index: 50
46	Literal
47	Variable
48	Variable
49	ExprTuple	50
50	Variable