Theorem strictly_decreasing_additions of type Forall ¶

from the theory of proveit.numbers.addition ¶

In [1]:

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.addition import strictly_decreasing_additions

In [2]:

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

Passed sanity check: strictly_decreasing_additions matches stored_expr

In [3]:

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

\forall_{i, j \in \mathbb{N}}~\left[\forall_{a_{1}, a_{2}, \ldots, a_{i}, c_{1}, c_{2}, \ldots, c_{j} \in \mathbb{R}^-}~\left[\forall_{b \in \mathbb{R}}~\left(\left(a_{1} +  a_{2} +  \ldots +  a_{i} + b+ c_{1} +  c_{2} +  \ldots +  c_{j}\right) < b\right)\right]\right]

In [4]:

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',)

In [5]:

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions
0	Operation	operator: 19 operand: 2
1	ExprTuple	2
2	Lambda	parameters: 3 body: 4
3	ExprTuple	49, 52
4	Conditional	value: 5 condition: 6
5	Operation	operator: 19 operand: 9
6	Operation	operator: 21 operands: 8
7	ExprTuple	9
8	ExprTuple	10, 11
9	Lambda	parameters: 12 body: 13
10	Operation	operator: 38 operands: 14
11	Operation	operator: 38 operands: 15
12	ExprTuple	45, 47
13	Conditional	value: 16 condition: 17
14	ExprTuple	49, 18
15	ExprTuple	52, 18
16	Operation	operator: 19 operand: 23
17	Operation	operator: 21 operands: 22
18	Literal
19	Literal
20	ExprTuple	23
21	Literal
22	ExprTuple	24, 25
23	Lambda	parameter: 46 body: 27
24	ExprRange	lambda_map: 28 start_index: 51 end_index: 49
25	ExprRange	lambda_map: 29 start_index: 51 end_index: 52
26	ExprTuple	46
27	Conditional	value: 30 condition: 31
28	Lambda	parameter: 58 body: 32
29	Lambda	parameter: 58 body: 33
30	Operation	operator: 34 operands: 35
31	Operation	operator: 38 operands: 36
32	Operation	operator: 38 operands: 37
33	Operation	operator: 38 operands: 39
34	Literal
35	ExprTuple	40, 46
36	ExprTuple	46, 41
37	ExprTuple	53, 42
38	Literal
39	ExprTuple	54, 42
40	Operation	operator: 43 operands: 44
41	Literal
42	Literal
43	Literal
44	ExprTuple	45, 46, 47
45	ExprRange	lambda_map: 48 start_index: 51 end_index: 49
46	Variable
47	ExprRange	lambda_map: 50 start_index: 51 end_index: 52
48	Lambda	parameter: 58 body: 53
49	Variable
50	Lambda	parameter: 58 body: 54
51	Literal
52	Variable
53	IndexedVar	variable: 55 index: 58
54	IndexedVar	variable: 56 index: 58
55	Variable
56	Variable
57	ExprTuple	58
58	Variable