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, Conditional, ExprRange, ExprTuple, IndexedVar, Lambda, 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 = ExprTuple(Lambda([A_1_to_m, B_1_to_m], 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(\left(A_{1}, A_{2}, \ldots, A_{m}, B_{1}, B_{2}, \ldots, B_{m}\right) \mapsto \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..\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: 2 body: 3
2	ExprTuple	22, 9
3	Conditional	value: 4 condition: 5
4	Operation	operator: 17 operands: 6
5	Operation	operator: 7 operands: 8
6	ExprTuple	9
7	Literal
8	ExprTuple	10, 11, 12, 13
9	ExprRange	lambda_map: 14 start_index: 28 end_index: 29
10	ExprRange	lambda_map: 15 start_index: 28 end_index: 29
11	ExprRange	lambda_map: 16 start_index: 28 end_index: 29
12	Operation	operator: 17 operands: 18
13	ExprRange	lambda_map: 19 start_index: 28 end_index: 29
14	Lambda	parameter: 38 body: 34
15	Lambda	parameter: 38 body: 20
16	Lambda	parameter: 38 body: 21
17	Literal
18	ExprTuple	22
19	Lambda	parameter: 38 body: 23
20	Operation	operator: 25 operands: 24
21	Operation	operator: 25 operands: 26
22	ExprRange	lambda_map: 27 start_index: 28 end_index: 29
23	Operation	operator: 30 operands: 31
24	ExprTuple	33, 32
25	Literal
26	ExprTuple	34, 32
27	Lambda	parameter: 38 body: 33
28	Literal
29	Variable
30	Literal
31	ExprTuple	33, 34
32	Literal
33	IndexedVar	variable: 35 index: 38
34	IndexedVar	variable: 36 index: 38
35	Variable
36	Variable
37	ExprTuple	38
38	Variable