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, ExprRange, ExprTuple, IndexedVar, Variable, m
from proveit.core_expr_types import A_1_to_m
from proveit.logic import 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(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} \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)

stored_expr.style_options()

name	description	default	current value	related methods
wrap_positions	position(s) at which wrapping is to occur; 'n' is after the nth comma.	()	()	('with_wrapping_at',)
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	left	left	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1, 2, 3, 4
1	ExprRange	lambda_map: 5 start_index: 18 end_index: 19
2	ExprRange	lambda_map: 6 start_index: 18 end_index: 19
3	Operation	operator: 7 operands: 8
4	ExprRange	lambda_map: 9 start_index: 18 end_index: 19
5	Lambda	parameter: 28 body: 10
6	Lambda	parameter: 28 body: 11
7	Literal
8	ExprTuple	12
9	Lambda	parameter: 28 body: 13
10	Operation	operator: 15 operands: 14
11	Operation	operator: 15 operands: 16
12	ExprRange	lambda_map: 17 start_index: 18 end_index: 19
13	Operation	operator: 20 operands: 21
14	ExprTuple	23, 22
15	Literal
16	ExprTuple	24, 22
17	Lambda	parameter: 28 body: 23
18	Literal
19	Variable
20	Literal
21	ExprTuple	23, 24
22	Literal
23	IndexedVar	variable: 25 index: 28
24	IndexedVar	variable: 26 index: 28
25	Variable
26	Variable
27	ExprTuple	28
28	Variable