Expression of type Equals

from the theory of proveit.logic.sets.enumeration

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, IndexedVar, Variable, a, b, c, m, n
from proveit.core_expr_types import a_1_to_m, c_1_to_n
from proveit.logic import Equals, InSet, Or, Set
from proveit.numbers import one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Equals(InSet(b, Set(a_1_to_m, b, c_1_to_n)), Or(ExprRange(sub_expr1, Equals(b, IndexedVar(a, sub_expr1)), one, m), Equals(b, b), ExprRange(sub_expr1, Equals(b, IndexedVar(c, sub_expr1)), one, n))).with_wrapping_at(2)

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())

\begin{array}{c} \begin{array}{l} \left(b \in \left\{a_{1}, a_{2}, \ldots, a_{m}, b,c_{1}, c_{2}, \ldots, c_{n}\right\}\right) =  \\ \left(\left(b = a_{1}\right) \lor  \left(b = a_{2}\right) \lor  \ldots \lor  \left(b = a_{m}\right) \lor \left(b = b\right)\lor \left(b = c_{1}\right) \lor  \left(b = c_{2}\right) \lor  \ldots \lor  \left(b = c_{n}\right)\right) \end{array} \end{array}

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.	()	(2)	('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: 27 operands: 1
1	ExprTuple	2, 3
2	Operation	operator: 4 operands: 5
3	Operation	operator: 6 operands: 7
4	Literal
5	ExprTuple	30, 8
6	Literal
7	ExprTuple	9, 10, 11
8	Operation	operator: 12 operands: 13
9	ExprRange	lambda_map: 14 start_index: 24 end_index: 22
10	Operation	operator: 27 operands: 15
11	ExprRange	lambda_map: 16 start_index: 24 end_index: 25
12	Literal
13	ExprTuple	17, 30, 18
14	Lambda	parameter: 35 body: 19
15	ExprTuple	30, 30
16	Lambda	parameter: 35 body: 20
17	ExprRange	lambda_map: 21 start_index: 24 end_index: 22
18	ExprRange	lambda_map: 23 start_index: 24 end_index: 25
19	Operation	operator: 27 operands: 26
20	Operation	operator: 27 operands: 28
21	Lambda	parameter: 35 body: 29
22	Variable
23	Lambda	parameter: 35 body: 31
24	Literal
25	Variable
26	ExprTuple	30, 29
27	Literal
28	ExprTuple	30, 31
29	IndexedVar	variable: 32 index: 35
30	Variable
31	IndexedVar	variable: 33 index: 35
32	Variable
33	Variable
34	ExprTuple	35
35	Variable