Theorem weak_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 weak_summation_from_summands_bound

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

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