Expression of type ExprTuple

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, ExprTuple, IndexedVar, Lambda, 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 = ExprTuple(Lambda([A_1_to_l, B_1_to_m, C_1_to_n], 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(\left(A_{1}, A_{2}, \ldots, A_{l}, B_{1}, B_{2}, \ldots, B_{m}, C_{1}, C_{2}, \ldots, C_{n}\right) \mapsto \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..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameters: 15 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9, 10
7	Literal
8	ExprTuple	11, 12, 13
9	Operation	operator: 25 operands: 14
10	Operation	operator: 25 operands: 15
11	ExprRange	lambda_map: 16 start_index: 40 end_index: 28
12	ExprRange	lambda_map: 17 start_index: 40 end_index: 41
13	ExprRange	lambda_map: 18 start_index: 40 end_index: 30
14	ExprTuple	20, 19, 21
15	ExprTuple	20, 35, 21
16	Lambda	parameter: 47 body: 22
17	Lambda	parameter: 47 body: 23
18	Lambda	parameter: 47 body: 24
19	Operation	operator: 25 operands: 26
20	ExprRange	lambda_map: 27 start_index: 40 end_index: 28
21	ExprRange	lambda_map: 29 start_index: 40 end_index: 30
22	Operation	operator: 33 operands: 31
23	Operation	operator: 33 operands: 32
24	Operation	operator: 33 operands: 34
25	Literal
26	ExprTuple	35
27	Lambda	parameter: 47 body: 36
28	Variable
29	Lambda	parameter: 47 body: 37
30	Variable
31	ExprTuple	36, 38
32	ExprTuple	44, 38
33	Literal
34	ExprTuple	37, 38
35	ExprRange	lambda_map: 39 start_index: 40 end_index: 41
36	IndexedVar	variable: 42 index: 47
37	IndexedVar	variable: 43 index: 47
38	Literal
39	Lambda	parameter: 47 body: 44
40	Literal
41	Variable
42	Variable
43	Variable
44	IndexedVar	variable: 45 index: 47
45	Variable
46	ExprTuple	47
47	Variable