Theorem less_add_both of type Forall

from the theory of proveit.numbers.ordering

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.ordering import less_add_both

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

Passed sanity check: less_add_both matches stored_expr

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

\forall_{a, b, c, d \in \mathbb{R}~|~a < b, c \leq d}~\left(\left(a + c\right) < \left(b + d\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: 1 operand: 3
1	Literal
2	ExprTuple	3
3	Lambda	parameters: 4 body: 5
4	ExprTuple	32, 33, 34, 35
5	Conditional	value: 6 condition: 7
6	Operation	operator: 27 operands: 8
7	Operation	operator: 9 operands: 10
8	ExprTuple	11, 12
9	Literal
10	ExprTuple	13, 14, 15, 16, 17, 18
11	Operation	operator: 20 operands: 19
12	Operation	operator: 20 operands: 21
13	Operation	operator: 25 operands: 22
14	Operation	operator: 25 operands: 23
15	Operation	operator: 25 operands: 24
16	Operation	operator: 25 operands: 26
17	Operation	operator: 27 operands: 28
18	Operation	operator: 29 operands: 30
19	ExprTuple	32, 34
20	Literal
21	ExprTuple	33, 35
22	ExprTuple	32, 31
23	ExprTuple	33, 31
24	ExprTuple	34, 31
25	Literal
26	ExprTuple	35, 31
27	Literal
28	ExprTuple	32, 33
29	Literal
30	ExprTuple	34, 35
31	Literal
32	Variable
33	Variable
34	Variable
35	Variable