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, 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
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_1_to_n), And(A_1_to_l, And(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} \land  A_{2} \land  \ldots \land  A_{l}\land B_{1} \land  B_{2} \land  \ldots \land  B_{m}\land C_{1} \land  C_{2} \land  \ldots \land  C_{n}\right) =  \\ \left(A_{1} \land  A_{2} \land  \ldots \land  A_{l} \land \left(B_{1} \land  B_{2} \land  \ldots \land  B_{m}\right)\land C_{1} \land  C_{2} \land  \ldots \land  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: 24 operands: 5
3	Literal
4	ExprTuple	6, 7
5	ExprTuple	8, 9, 10
6	Operation	operator: 24 operands: 11
7	Operation	operator: 24 operands: 12
8	ExprRange	lambda_map: 13 start_index: 37 end_index: 23
9	ExprRange	lambda_map: 14 start_index: 37 end_index: 38
10	ExprRange	lambda_map: 15 start_index: 37 end_index: 27
11	ExprTuple	16, 32, 18
12	ExprTuple	16, 17, 18
13	Lambda	parameter: 44 body: 19
14	Lambda	parameter: 44 body: 20
15	Lambda	parameter: 44 body: 21
16	ExprRange	lambda_map: 22 start_index: 37 end_index: 23
17	Operation	operator: 24 operands: 25
18	ExprRange	lambda_map: 26 start_index: 37 end_index: 27
19	Operation	operator: 30 operands: 28
20	Operation	operator: 30 operands: 29
21	Operation	operator: 30 operands: 31
22	Lambda	parameter: 44 body: 33
23	Variable
24	Literal
25	ExprTuple	32
26	Lambda	parameter: 44 body: 34
27	Variable
28	ExprTuple	33, 35
29	ExprTuple	41, 35
30	Literal
31	ExprTuple	34, 35
32	ExprRange	lambda_map: 36 start_index: 37 end_index: 38
33	IndexedVar	variable: 39 index: 44
34	IndexedVar	variable: 40 index: 44
35	Literal
36	Lambda	parameter: 44 body: 41
37	Literal
38	Variable
39	Variable
40	Variable
41	IndexedVar	variable: 42 index: 44
42	Variable
43	ExprTuple	44
44	Variable