Expression of type Forall

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

# build up the expression from sub-expressions
expr = 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))

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())

\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)

stored_expr.style_options()

name	description	default	current value	related methods
with_wrapping	If 'True', wrap the Expression after the parameters	None	None/False	('with_wrapping',)
condition_wrapping	Wrap 'before' or 'after' the condition (or None).	None	None/False	('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_params	If 'True', wraps every two parameters AND wraps the Expression after the parameters	None	None/False	('with_params',)
justification	justify to the 'left', 'center', or 'right' in the array cells	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

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