Theorem rescale_interval_oc_membership of type Forall

from the theory of proveit.numbers.number_sets.real_numbers

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.number_sets.real_numbers import rescale_interval_oc_membership

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

Passed sanity check: rescale_interval_oc_membership matches stored_expr

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

\forall_{a, b, c \in \mathbb{R}}~\left[\forall_{x \in \left(a,b\right]}~\left(\left(c \cdot x\right) \in \left(c \cdot a,c \cdot b\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: 7 operand: 2
1	ExprTuple	2
2	Lambda	parameters: 3 body: 4
3	ExprTuple	39, 41, 40
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, 14
11	Lambda	parameter: 33 body: 16
12	Operation	operator: 24 operands: 17
13	Operation	operator: 24 operands: 18
14	Operation	operator: 24 operands: 19
15	ExprTuple	33
16	Conditional	value: 20 condition: 21
17	ExprTuple	39, 22
18	ExprTuple	41, 22
19	ExprTuple	40, 22
20	Operation	operator: 24 operands: 23
21	Operation	operator: 24 operands: 25
22	Literal
23	ExprTuple	26, 27
24	Literal
25	ExprTuple	33, 28
26	Operation	operator: 37 operands: 29
27	Operation	operator: 31 operands: 30
28	Operation	operator: 31 operands: 32
29	ExprTuple	40, 33
30	ExprTuple	34, 35
31	Literal
32	ExprTuple	39, 41
33	Variable
34	Operation	operator: 37 operands: 36
35	Operation	operator: 37 operands: 38
36	ExprTuple	40, 39
37	Literal
38	ExprTuple	40, 41
39	Variable
40	Variable
41	Variable