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 i
from proveit.core_expr_types import a_1_to_i
from proveit.logic import Forall, InSet
from proveit.numbers import Add, Natural, RealNonPos

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

\forall_{i \in \mathbb{N}}~\left[\forall_{a_{1}, a_{2}, \ldots, a_{i} \in \mathbb{R}^{\le 0}}~\left(\left(a_{1} +  a_{2} +  \ldots +  a_{i}\right) \in \mathbb{R}^{\le 0}\right)\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: 7 operand: 2
1	ExprTuple	2
2	Lambda	parameter: 27 body: 4
3	ExprTuple	27
4	Conditional	value: 5 condition: 6
5	Operation	operator: 7 operand: 10
6	Operation	operator: 28 operands: 9
7	Literal
8	ExprTuple	10
9	ExprTuple	27, 11
10	Lambda	parameters: 21 body: 12
11	Literal
12	Conditional	value: 13 condition: 14
13	Operation	operator: 28 operands: 15
14	Operation	operator: 16 operands: 17
15	ExprTuple	18, 31
16	Literal
17	ExprTuple	19
18	Operation	operator: 20 operands: 21
19	ExprRange	lambda_map: 22 start_index: 26 end_index: 27
20	Literal
21	ExprTuple	23
22	Lambda	parameter: 34 body: 24
23	ExprRange	lambda_map: 25 start_index: 26 end_index: 27
24	Operation	operator: 28 operands: 29
25	Lambda	parameter: 34 body: 30
26	Literal
27	Variable
28	Literal
29	ExprTuple	30, 31
30	IndexedVar	variable: 32 index: 34
31	Literal
32	Variable
33	ExprTuple	34
34	Variable