Expression of type Equals

from the theory of proveit.numbers.numerals.decimals

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, Lambda, Variable
from proveit.core_expr_types import Len
from proveit.logic import Equals
from proveit.numbers import eight, five, four, nine, one, seven, six, three, two

# build up the expression from sub-expressions
sub_expr1 = Variable("_b", latex_format = r"{_{-}b}")
sub_expr2 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr3 = Lambda(sub_expr1, seven)
expr = Equals(Len(operands = [Lambda(sub_expr1, three), Lambda(sub_expr1, eight), Lambda(sub_expr1, six), sub_expr3, Lambda(sub_expr1, four), Lambda(sub_expr2, nine), Lambda(sub_expr1, five), sub_expr3, Lambda(sub_expr1, two)]), Len(operands = [ExprRange(sub_expr2, sub_expr2, one, nine)]))

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} \mapsto 3, {_{-}b} \mapsto 8, {_{-}b} \mapsto 6, {_{-}b} \mapsto 7, {_{-}b} \mapsto 4, {_{-}a} \mapsto 9, {_{-}b} \mapsto 5, {_{-}b} \mapsto 7, {_{-}b} \mapsto 2\right)| = |\left(1, 2, \ldots, 9\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: 1 operands: 2
1	Literal
2	ExprTuple	3, 4
3	Operation	operator: 6 operands: 5
4	Operation	operator: 6 operands: 7
5	ExprTuple	8, 9, 10, 14, 11, 12, 13, 14, 15
6	Literal
7	ExprTuple	16
8	Lambda	parameter: 28 body: 17
9	Lambda	parameter: 28 body: 18
10	Lambda	parameter: 28 body: 19
11	Lambda	parameter: 28 body: 20
12	Lambda	parameter: 30 body: 27
13	Lambda	parameter: 28 body: 21
14	Lambda	parameter: 28 body: 22
15	Lambda	parameter: 28 body: 24
16	ExprRange	lambda_map: 25 start_index: 26 end_index: 27
17	Literal
18	Literal
19	Literal
20	Literal
21	Literal
22	Literal
23	ExprTuple	28
24	Literal
25	Lambda	parameter: 30 body: 30
26	Literal
27	Literal
28	Variable
29	ExprTuple	30
30	Variable