Axiom transitivity_less_less 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_axiom_expr # Load the stored axiom expression as 'stored_expr'
# import the special expression
from proveit.numbers.ordering import transitivity_less_less

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

Passed sanity check: transitivity_less_less matches stored_expr

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

\forall_{x, y, z~|~x < y, y < z}~\left(x < z\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	16, 17, 18
5	Conditional	value: 6 condition: 7
6	Operation	operator: 14 operands: 8
7	Operation	operator: 9 operands: 10
8	ExprTuple	16, 18
9	Literal
10	ExprTuple	11, 12
11	Operation	operator: 14 operands: 13
12	Operation	operator: 14 operands: 15
13	ExprTuple	16, 17
14	Literal
15	ExprTuple	17, 18
16	Variable
17	Variable
18	Variable