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, m, n
from proveit.core_expr_types import A_1_to_m, C_1_to_n
from proveit.logic import And, Boolean, 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_m, B, C_1_to_n], Conditional(Or(A_1_to_m, B, C_1_to_n), And(ExprRange(sub_expr1, InSet(IndexedVar(A, sub_expr1), Boolean), one, m), InSet(B, Boolean), ExprRange(sub_expr1, InSet(IndexedVar(C, sub_expr1), Boolean), one, n), B))))

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