Expression of type Conditional

from the theory of proveit.logic.booleans.disjunction

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 A, B, C, Conditional, ExprRange, IndexedVar, Variable, l, m, n
from proveit.core_expr_types import A_1_to_l, B_1_to_m, C_1_to_n
from proveit.logic import And, Boolean, Equals, InSet, Or
from proveit.numbers import one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Conditional(Equals(Or(A_1_to_l, Or(B_1_to_m), C_1_to_n), Or(A_1_to_l, B_1_to_m, C_1_to_n)).with_wrapping_at(2), And(ExprRange(sub_expr1, InSet(IndexedVar(A, sub_expr1), Boolean), one, l), ExprRange(sub_expr1, InSet(IndexedVar(B, sub_expr1), Boolean), one, m), ExprRange(sub_expr1, InSet(IndexedVar(C, sub_expr1), Boolean), 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\{\begin{array}{c} \begin{array}{l} \left(A_{1} \lor  A_{2} \lor  \ldots \lor  A_{l} \lor \left(B_{1} \lor  B_{2} \lor  \ldots \lor  B_{m}\right)\lor C_{1} \lor  C_{2} \lor  \ldots \lor  C_{n}\right) =  \\ \left(A_{1} \lor  A_{2} \lor  \ldots \lor  A_{l}\lor B_{1} \lor  B_{2} \lor  \ldots \lor  B_{m}\lor C_{1} \lor  C_{2} \lor  \ldots \lor  C_{n}\right) \end{array} \end{array} \textrm{ if } \left(A_{1} \in \mathbb{B}\right) ,  \left(A_{2} \in \mathbb{B}\right) ,  \ldots ,  \left(A_{l} \in \mathbb{B}\right), \left(B_{1} \in \mathbb{B}\right) ,  \left(B_{2} \in \mathbb{B}\right) ,  \ldots ,  \left(B_{m} \in \mathbb{B}\right), \left(C_{1} \in \mathbb{B}\right) ,  \left(C_{2} \in \mathbb{B}\right) ,  \ldots ,  \left(C_{n} \in \mathbb{B}\right)\right..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Conditional	value: 1 condition: 2
1	Operation	operator: 3 operands: 4
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7, 8
5	Literal
6	ExprTuple	9, 10, 11
7	Operation	operator: 23 operands: 12
8	Operation	operator: 23 operands: 13
9	ExprRange	lambda_map: 14 start_index: 38 end_index: 26
10	ExprRange	lambda_map: 15 start_index: 38 end_index: 39
11	ExprRange	lambda_map: 16 start_index: 38 end_index: 28
12	ExprTuple	18, 17, 19
13	ExprTuple	18, 33, 19
14	Lambda	parameter: 45 body: 20
15	Lambda	parameter: 45 body: 21
16	Lambda	parameter: 45 body: 22
17	Operation	operator: 23 operands: 24
18	ExprRange	lambda_map: 25 start_index: 38 end_index: 26
19	ExprRange	lambda_map: 27 start_index: 38 end_index: 28
20	Operation	operator: 31 operands: 29
21	Operation	operator: 31 operands: 30
22	Operation	operator: 31 operands: 32
23	Literal
24	ExprTuple	33
25	Lambda	parameter: 45 body: 34
26	Variable
27	Lambda	parameter: 45 body: 35
28	Variable
29	ExprTuple	34, 36
30	ExprTuple	42, 36
31	Literal
32	ExprTuple	35, 36
33	ExprRange	lambda_map: 37 start_index: 38 end_index: 39
34	IndexedVar	variable: 40 index: 45
35	IndexedVar	variable: 41 index: 45
36	Literal
37	Lambda	parameter: 45 body: 42
38	Literal
39	Variable
40	Variable
41	Variable
42	IndexedVar	variable: 43 index: 45
43	Variable
44	ExprTuple	45
45	Variable