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, m, n
from proveit.core_expr_types import A_1_to_m, C_1_to_n
from proveit.logic import And, Boolean, InSet, Or
from proveit.numbers import one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Conditional(Or(A_1_to_m, B, C_1_to_n), And(ExprRange(sub_expr1, InSet(IndexedVar(A, sub_expr1), Boolean), one, m), InSet(B, Boolean), ExprRange(sub_expr1, InSet(IndexedVar(C, sub_expr1), Boolean), one, n), B))

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\{A_{1} \lor  A_{2} \lor  \ldots \lor  A_{m} \lor B\lor C_{1} \lor  C_{2} \lor  \ldots \lor  C_{n} \textrm{ if } \left(A_{1} \in \mathbb{B}\right) ,  \left(A_{2} \in \mathbb{B}\right) ,  \ldots ,  \left(A_{m} \in \mathbb{B}\right) ,  B \in \mathbb{B}, \left(C_{1} \in \mathbb{B}\right) ,  \left(C_{2} \in \mathbb{B}\right) ,  \ldots ,  \left(C_{n} \in \mathbb{B}\right) ,  B\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, 21, 8
5	Literal
6	ExprTuple	9, 10, 11, 21
7	ExprRange	lambda_map: 12 start_index: 18 end_index: 15
8	ExprRange	lambda_map: 13 start_index: 18 end_index: 19
9	ExprRange	lambda_map: 14 start_index: 18 end_index: 15
10	Operation	operator: 24 operands: 16
11	ExprRange	lambda_map: 17 start_index: 18 end_index: 19
12	Lambda	parameter: 32 body: 26
13	Lambda	parameter: 32 body: 27
14	Lambda	parameter: 32 body: 20
15	Variable
16	ExprTuple	21, 28
17	Lambda	parameter: 32 body: 22
18	Literal
19	Variable
20	Operation	operator: 24 operands: 23
21	Variable
22	Operation	operator: 24 operands: 25
23	ExprTuple	26, 28
24	Literal
25	ExprTuple	27, 28
26	IndexedVar	variable: 29 index: 32
27	IndexedVar	variable: 30 index: 32
28	Literal
29	Variable
30	Variable
31	ExprTuple	32
32	Variable