Expression of type Or

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.logic import Equals, Or
from proveit.numbers import one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = 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))

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_{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)

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',)

# 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, 5
3	ExprRange	lambda_map: 6 start_index: 10 end_index: 7
4	Operation	operator: 15 operands: 8
5	ExprRange	lambda_map: 9 start_index: 10 end_index: 11
6	Lambda	parameter: 23 body: 12
7	Variable
8	ExprTuple	18, 18
9	Lambda	parameter: 23 body: 13
10	Literal
11	Variable
12	Operation	operator: 15 operands: 14
13	Operation	operator: 15 operands: 16
14	ExprTuple	18, 17
15	Literal
16	ExprTuple	18, 19
17	IndexedVar	variable: 20 index: 23
18	Variable
19	IndexedVar	variable: 21 index: 23
20	Variable
21	Variable
22	ExprTuple	23
23	Variable