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.core_expr_types import a_1_to_i
from proveit.logic import Forall, InSet
from proveit.numbers import Add, RationalNeg

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [a_1_to_i], instance_expr = InSet(Add(a_1_to_i), RationalNeg), domain = RationalNeg)

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} \in \mathbb{Q}^-}~\left(\left(a_{1} +  a_{2} +  \ldots +  a_{i}\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: 13 body: 4
4	Conditional	value: 5 condition: 6
5	Operation	operator: 20 operands: 7
6	Operation	operator: 8 operands: 9
7	ExprTuple	10, 23
8	Literal
9	ExprTuple	11
10	Operation	operator: 12 operands: 13
11	ExprRange	lambda_map: 14 start_index: 18 end_index: 19
12	Literal
13	ExprTuple	15
14	Lambda	parameter: 26 body: 16
15	ExprRange	lambda_map: 17 start_index: 18 end_index: 19
16	Operation	operator: 20 operands: 21
17	Lambda	parameter: 26 body: 22
18	Literal
19	Variable
20	Literal
21	ExprTuple	22, 23
22	IndexedVar	variable: 24 index: 26
23	Literal
24	Variable
25	ExprTuple	26
26	Variable