Expression of type Conditional

from the theory of proveit.logic.booleans.conjunction

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, D, ExprRange, IndexedVar, Variable, l, m, n
from proveit.core_expr_types import A_1_to_l, B_1_to_m, D_1_to_n
from proveit.logic import And, Boolean, Equals, InSet
from proveit.numbers import one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Conditional(Equals(And(A_1_to_l, B_1_to_m, C, D_1_to_n), And(A_1_to_l, C, B_1_to_m, D_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), InSet(C, Boolean), ExprRange(sub_expr1, InSet(IndexedVar(D, 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} \land  A_{2} \land  \ldots \land  A_{l}\land B_{1} \land  B_{2} \land  \ldots \land  B_{m} \land C\land D_{1} \land  D_{2} \land  \ldots \land  D_{n}\right) =  \\ \left(A_{1} \land  A_{2} \land  \ldots \land  A_{l} \land C\land B_{1} \land  B_{2} \land  \ldots \land  B_{m}\land D_{1} \land  D_{2} \land  \ldots \land  D_{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) ,  C \in \mathbb{B}, \left(D_{1} \in \mathbb{B}\right) ,  \left(D_{2} \in \mathbb{B}\right) ,  \ldots ,  \left(D_{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: 13 operands: 5
3	Literal
4	ExprTuple	6, 7
5	ExprTuple	8, 9, 10, 11
6	Operation	operator: 13 operands: 12
7	Operation	operator: 13 operands: 14
8	ExprRange	lambda_map: 15 start_index: 31 end_index: 27
9	ExprRange	lambda_map: 16 start_index: 31 end_index: 29
10	Operation	operator: 35 operands: 17
11	ExprRange	lambda_map: 18 start_index: 31 end_index: 32
12	ExprTuple	19, 20, 24, 21
13	Literal
14	ExprTuple	19, 24, 20, 21
15	Lambda	parameter: 45 body: 22
16	Lambda	parameter: 45 body: 23
17	ExprTuple	24, 40
18	Lambda	parameter: 45 body: 25
19	ExprRange	lambda_map: 26 start_index: 31 end_index: 27
20	ExprRange	lambda_map: 28 start_index: 31 end_index: 29
21	ExprRange	lambda_map: 30 start_index: 31 end_index: 32
22	Operation	operator: 35 operands: 33
23	Operation	operator: 35 operands: 34
24	Variable
25	Operation	operator: 35 operands: 36
26	Lambda	parameter: 45 body: 37
27	Variable
28	Lambda	parameter: 45 body: 38
29	Variable
30	Lambda	parameter: 45 body: 39
31	Literal
32	Variable
33	ExprTuple	37, 40
34	ExprTuple	38, 40
35	Literal
36	ExprTuple	39, 40
37	IndexedVar	variable: 41 index: 45
38	IndexedVar	variable: 42 index: 45
39	IndexedVar	variable: 43 index: 45
40	Literal
41	Variable
42	Variable
43	Variable
44	ExprTuple	45
45	Variable