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, Not, Or
from proveit.numbers import one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = IndexedVar(B, sub_expr1)
sub_expr3 = IndexedVar(A, sub_expr1)
expr = ExprTuple(Lambda([A_1_to_m, B_1_to_m], Conditional(Or(ExprRange(sub_expr1, Not(sub_expr2), one, m)), And(ExprRange(sub_expr1, InSet(sub_expr3, Boolean), one, m), ExprRange(sub_expr1, InSet(sub_expr2, Boolean), one, m), Or(ExprRange(sub_expr1, Not(sub_expr3), one, m)), ExprRange(sub_expr1, Implies(sub_expr3, sub_expr2), 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\{(\lnot B_{1}) \lor  (\lnot B_{2}) \lor  \ldots \lor  (\lnot 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) ,  (\lnot A_{1}) \lor  (\lnot A_{2}) \lor  \ldots \lor  (\lnot 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	4, 5
3	Conditional	value: 6 condition: 7
4	ExprRange	lambda_map: 8 start_index: 34 end_index: 35
5	ExprRange	lambda_map: 9 start_index: 34 end_index: 35
6	Operation	operator: 21 operands: 10
7	Operation	operator: 11 operands: 12
8	Lambda	parameter: 47 body: 44
9	Lambda	parameter: 47 body: 40
10	ExprTuple	13
11	Literal
12	ExprTuple	14, 15, 16, 17
13	ExprRange	lambda_map: 18 start_index: 34 end_index: 35
14	ExprRange	lambda_map: 19 start_index: 34 end_index: 35
15	ExprRange	lambda_map: 20 start_index: 34 end_index: 35
16	Operation	operator: 21 operands: 22
17	ExprRange	lambda_map: 23 start_index: 34 end_index: 35
18	Lambda	parameter: 47 body: 24
19	Lambda	parameter: 47 body: 25
20	Lambda	parameter: 47 body: 26
21	Literal
22	ExprTuple	27
23	Lambda	parameter: 47 body: 28
24	Operation	operator: 41 operand: 40
25	Operation	operator: 31 operands: 30
26	Operation	operator: 31 operands: 32
27	ExprRange	lambda_map: 33 start_index: 34 end_index: 35
28	Operation	operator: 36 operands: 37
29	ExprTuple	40
30	ExprTuple	44, 38
31	Literal
32	ExprTuple	40, 38
33	Lambda	parameter: 47 body: 39
34	Literal
35	Variable
36	Literal
37	ExprTuple	44, 40
38	Literal
39	Operation	operator: 41 operand: 44
40	IndexedVar	variable: 43 index: 47
41	Literal
42	ExprTuple	44
43	Variable
44	IndexedVar	variable: 45 index: 47
45	Variable
46	ExprTuple	47
47	Variable