Expression of type Forall

from the theory of proveit.numbers.absolute_value

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 a, b, c
from proveit.logic import And, Forall
from proveit.numbers import Abs, LessEq, Max, Real

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [a, b, c], instance_expr = LessEq(Abs(a), Max(Abs(b), Abs(c))), domain = Real, condition = And(LessEq(b, a), LessEq(a, c)).with_total_ordering_style())

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())

\forall_{a, b, c \in \mathbb{R}~|~b \leq a \leq c}~\left(\left|a\right| \leq {\rm Max}\left(\left|b\right|, \left|c\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: 1 operand: 3
1	Literal
2	ExprTuple	3
3	Lambda	parameters: 4 body: 5
4	ExprTuple	37, 36, 38
5	Conditional	value: 6 condition: 7
6	Operation	operator: 34 operands: 8
7	Operation	operator: 23 operands: 9
8	ExprTuple	10, 11
9	ExprTuple	12, 13, 14, 15
10	Operation	operator: 31 operand: 37
11	Operation	operator: 17 operands: 18
12	Operation	operator: 21 operands: 19
13	Operation	operator: 21 operands: 20
14	Operation	operator: 21 operands: 22
15	Operation	operator: 23 operands: 24
16	ExprTuple	37
17	Literal
18	ExprTuple	25, 26
19	ExprTuple	37, 27
20	ExprTuple	36, 27
21	Literal
22	ExprTuple	38, 27
23	Literal
24	ExprTuple	28, 29
25	Operation	operator: 31 operand: 36
26	Operation	operator: 31 operand: 38
27	Literal
28	Operation	operator: 34 operands: 33
29	Operation	operator: 34 operands: 35
30	ExprTuple	36
31	Literal
32	ExprTuple	38
33	ExprTuple	36, 37
34	Literal
35	ExprTuple	37, 38
36	Variable
37	Variable
38	Variable