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, Conditional, ExprRange, IndexedVar, Variable, m
from proveit.core_expr_types import A_1_to_m, B_1_to_m
from proveit.logic import And, Boolean, Implies, InSet, Or
from proveit.numbers import one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = IndexedVar(A, sub_expr1)
sub_expr3 = IndexedVar(B, sub_expr1)
expr = Conditional(Or(B_1_to_m), And(ExprRange(sub_expr1, InSet(sub_expr2, Boolean), one, m), ExprRange(sub_expr1, InSet(sub_expr3, Boolean), one, m), Or(A_1_to_m), ExprRange(sub_expr1, Implies(sub_expr2, sub_expr3), one, m)))

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_{1} \lor  B_{2} \lor  \ldots \lor  B_{m} \textrm{ if } \left(A_{1} \in \mathbb{B}\right) ,  \left(A_{2} \in \mathbb{B}\right) ,  \ldots ,  \left(A_{m} \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) ,  A_{1} \lor  A_{2} \lor  \ldots \lor  A_{m}, \left(A_{1} \Rightarrow B_{1}\right) ,  \left(A_{2} \Rightarrow B_{2}\right) ,  \ldots ,  \left(A_{m} \Rightarrow B_{m}\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: 14 operands: 3
2	Operation	operator: 4 operands: 5
3	ExprTuple	6
4	Literal
5	ExprTuple	7, 8, 9, 10
6	ExprRange	lambda_map: 11 start_index: 25 end_index: 26
7	ExprRange	lambda_map: 12 start_index: 25 end_index: 26
8	ExprRange	lambda_map: 13 start_index: 25 end_index: 26
9	Operation	operator: 14 operands: 15
10	ExprRange	lambda_map: 16 start_index: 25 end_index: 26
11	Lambda	parameter: 35 body: 31
12	Lambda	parameter: 35 body: 17
13	Lambda	parameter: 35 body: 18
14	Literal
15	ExprTuple	19
16	Lambda	parameter: 35 body: 20
17	Operation	operator: 22 operands: 21
18	Operation	operator: 22 operands: 23
19	ExprRange	lambda_map: 24 start_index: 25 end_index: 26
20	Operation	operator: 27 operands: 28
21	ExprTuple	30, 29
22	Literal
23	ExprTuple	31, 29
24	Lambda	parameter: 35 body: 30
25	Literal
26	Variable
27	Literal
28	ExprTuple	30, 31
29	Literal
30	IndexedVar	variable: 32 index: 35
31	IndexedVar	variable: 33 index: 35
32	Variable
33	Variable
34	ExprTuple	35
35	Variable