Expression of type Conditional

from the theory of proveit.numbers.number_sets.real_numbers

import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import Conditional, a, b, c, x
from proveit.logic import And, Forall, InSet
from proveit.numbers import IntervalCO, Mult, Real

# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [x], instance_expr = InSet(Mult(c, x), IntervalCO(Mult(c, a), Mult(c, b))), domain = IntervalCO(a, b)), And(InSet(a, Real), InSet(b, Real), InSet(c, Real)))

expr:

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

Passed sanity check: expr matches stored_expr

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

\left\{\forall_{x \in \left[a,b\right)}~\left(\left(c \cdot x\right) \in \left[c \cdot a,c \cdot b\right)\right) \textrm{ if } a \in \mathbb{R} ,  b \in \mathbb{R} ,  c \in \mathbb{R}\right..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Conditional	value: 1 condition: 2
1	Operation	operator: 3 operand: 7
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7
5	Literal
6	ExprTuple	8, 9, 10
7	Lambda	parameter: 29 body: 12
8	Operation	operator: 20 operands: 13
9	Operation	operator: 20 operands: 14
10	Operation	operator: 20 operands: 15
11	ExprTuple	29
12	Conditional	value: 16 condition: 17
13	ExprTuple	35, 18
14	ExprTuple	37, 18
15	ExprTuple	36, 18
16	Operation	operator: 20 operands: 19
17	Operation	operator: 20 operands: 21
18	Literal
19	ExprTuple	22, 23
20	Literal
21	ExprTuple	29, 24
22	Operation	operator: 33 operands: 25
23	Operation	operator: 27 operands: 26
24	Operation	operator: 27 operands: 28
25	ExprTuple	36, 29
26	ExprTuple	30, 31
27	Literal
28	ExprTuple	35, 37
29	Variable
30	Operation	operator: 33 operands: 32
31	Operation	operator: 33 operands: 34
32	ExprTuple	36, 35
33	Literal
34	ExprTuple	36, 37
35	Variable
36	Variable
37	Variable