Expression of type LessEq

from the theory of proveit.numbers.modular

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 N, a, b
from proveit.numbers import ModAbs, greater_eq, subtract

# build up the expression from sub-expressions
expr = greater_eq(ModAbs(subtract(a, b), N), subtract(ModAbs(a, N), ModAbs(b, N)))

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|a - b\right|_{\textup{mod}\thinspace N} \geq \left(\left|a\right|_{\textup{mod}\thinspace N} - \left|b\right|_{\textup{mod}\thinspace N}\right)

stored_expr.style_options()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix
wrap_positions	position(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.	()	()	('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)
direction	Direction of the relation (normal or reversed)	normal	reversed	('with_direction_reversed', 'is_reversed')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operands: 2
1	Literal
2	ExprTuple	3, 4
3	Operation	operator: 12 operands: 5
4	Operation	operator: 17 operands: 6
5	ExprTuple	7, 8
6	ExprTuple	9, 21
7	Operation	operator: 17 operands: 10
8	Operation	operator: 19 operand: 14
9	Operation	operator: 12 operands: 13
10	ExprTuple	15, 21
11	ExprTuple	14
12	Literal
13	ExprTuple	15, 16
14	Operation	operator: 17 operands: 18
15	Variable
16	Operation	operator: 19 operand: 22
17	Literal
18	ExprTuple	22, 21
19	Literal
20	ExprTuple	22
21	Variable
22	Variable