Theorem strong_summation_from_summands_bound of type Forall

from the theory of proveit.numbers.summation

see dependencies

import proveit
# Automation is not needed when only building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_theorem_expr # Load the stored theorem expression as 'stored_expr'
# import the special expression
from proveit.numbers.summation import strong_summation_from_summands_bound

# check that the built expression is the same as the stored expression
assert strong_summation_from_summands_bound.expr == stored_expr
assert strong_summation_from_summands_bound.expr._style_id == stored_expr._style_id
print("Passed sanity check: strong_summation_from_summands_bound matches stored_expr")

Passed sanity check: strong_summation_from_summands_bound matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\forall_{a, b, S~|~|S| > 0}~\left(\left[\forall_{k \in S}~\left(a\left(k\right) < b\left(k\right)\right)\right] \Rightarrow \left(\left[\sum_{l \in S}~a\left(l\right)\right] < \left[\sum_{l \in S}~b\left(l\right)\right]\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: 14 operand: 2
1	ExprTuple	2
2	Lambda	parameters: 3 body: 4
3	ExprTuple	41, 42, 48
4	Conditional	value: 5 condition: 6
5	Operation	operator: 7 operands: 8
6	Operation	operator: 30 operands: 9
7	Literal
8	ExprTuple	10, 11
9	ExprTuple	12, 13
10	Operation	operator: 14 operand: 19
11	Operation	operator: 30 operands: 16
12	Literal
13	Operation	operator: 17 operand: 48
14	Literal
15	ExprTuple	19
16	ExprTuple	20, 21
17	Literal
18	ExprTuple	48
19	Lambda	parameter: 46 body: 22
20	Operation	operator: 24 operand: 28
21	Operation	operator: 24 operand: 29
22	Conditional	value: 26 condition: 27
23	ExprTuple	28
24	Literal
25	ExprTuple	29
26	Operation	operator: 30 operands: 31
27	Operation	operator: 44 operands: 32
28	Lambda	parameter: 47 body: 33
29	Lambda	parameter: 47 body: 34
30	Literal
31	ExprTuple	35, 36
32	ExprTuple	46, 48
33	Conditional	value: 37 condition: 39
34	Conditional	value: 38 condition: 39
35	Operation	operator: 41 operand: 46
36	Operation	operator: 42 operand: 46
37	Operation	operator: 41 operand: 47
38	Operation	operator: 42 operand: 47
39	Operation	operator: 44 operands: 45
40	ExprTuple	46
41	Variable
42	Variable
43	ExprTuple	47
44	Literal
45	ExprTuple	47, 48
46	Variable
47	Variable
48	Variable