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
from proveit.numbers import Add, Real, RealNonNeg, greater_eq

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [a_1_to_i, c_1_to_j], instance_expr = Forall(instance_param_or_params = [b], instance_expr = greater_eq(Add(a_1_to_i, b, c_1_to_j), b), domain = Real), domain = RealNonNeg)

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