Expression of type Equals

from the theory of proveit.numbers.ordering

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 ExprRange, Variable, a, b, c, d, e
from proveit.core_expr_types import Len
from proveit.logic import Equals
from proveit.numbers import Less, LessEq, four, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Equals(Len(operands = [Less(b, a), LessEq(a, c), Equals(c, d), LessEq(d, e)]), Len(operands = [ExprRange(sub_expr1, sub_expr1, one, four)]))

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(b < a, a \leq c, c = d, d \leq e\right)| = |\left(1, 2, \ldots, 4\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	normal	('with_direction_reversed', 'is_reversed')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 15 operands: 1
1	ExprTuple	2, 3
2	Operation	operator: 5 operands: 4
3	Operation	operator: 5 operands: 6
4	ExprTuple	7, 8, 9, 10
5	Literal
6	ExprTuple	11
7	Operation	operator: 12 operands: 13
8	Operation	operator: 17 operands: 14
9	Operation	operator: 15 operands: 16
10	Operation	operator: 17 operands: 18
11	ExprRange	lambda_map: 19 start_index: 20 end_index: 21
12	Literal
13	ExprTuple	22, 23
14	ExprTuple	23, 24
15	Literal
16	ExprTuple	24, 25
17	Literal
18	ExprTuple	25, 26
19	Lambda	parameter: 28 body: 28
20	Literal
21	Literal
22	Variable
23	Variable
24	Variable
25	Variable
26	Variable
27	ExprTuple	28
28	Variable