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, ExprRange, ExprTuple, IndexedVar, Variable, m
from proveit.core_expr_types import A_1_to_m
from proveit.logic import Boolean, Forall, InSet, Or
from proveit.numbers import Add, NaturalPos, one, two

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = IndexedVar(A, one)
sub_expr3 = IndexedVar(A, sub_expr1)
sub_expr4 = Add(m, one)
expr = ExprTuple(Forall(instance_param_or_params = [sub_expr2], instance_expr = InSet(sub_expr2, Boolean), domain = Boolean), Forall(instance_param_or_params = [m], instance_expr = Forall(instance_param_or_params = [ExprRange(sub_expr1, sub_expr3, one, Add(m, two))], instance_expr = InSet(Or(ExprRange(sub_expr1, sub_expr3, one, sub_expr4)), Boolean), condition = ExprRange(sub_expr1, InSet(sub_expr3, Boolean), one, sub_expr4)), domain = NaturalPos, condition = Forall(instance_param_or_params = [A_1_to_m], instance_expr = InSet(Or(A_1_to_m), Boolean), domain = Boolean)))

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(\forall_{A_{1} \in \mathbb{B}}~\left(A_{1} \in \mathbb{B}\right), \forall_{m \in \mathbb{N}^+~|~\forall_{A_{1}, A_{2}, \ldots, A_{m} \in \mathbb{B}}~\left(\left(A_{1} \lor  A_{2} \lor  \ldots \lor  A_{m}\right) \in \mathbb{B}\right)}~\left[\forall_{A_{1}, A_{2}, \ldots, A_{m + 2}~|~\left(A_{1} \in \mathbb{B}\right), \left(A_{2} \in \mathbb{B}\right), \ldots, \left(A_{m + 1} \in \mathbb{B}\right)}~\left(\left(A_{1} \lor  A_{2} \lor  \ldots \lor  A_{m + 1}\right) \in \mathbb{B}\right)\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
1	Operation	operator: 25 operand: 5
2	Operation	operator: 25 operand: 6
3	ExprTuple	5
4	ExprTuple	6
5	Lambda	parameter: 17 body: 8
6	Lambda	parameter: 59 body: 10
7	ExprTuple	17
8	Conditional	value: 11 condition: 11
9	ExprTuple	59
10	Conditional	value: 12 condition: 13
11	Operation	operator: 60 operands: 14
12	Operation	operator: 25 operand: 18
13	Operation	operator: 44 operands: 16
14	ExprTuple	17, 63
15	ExprTuple	18
16	ExprTuple	19, 20
17	IndexedVar	variable: 64 index: 58
18	Lambda	parameters: 22 body: 23
19	Operation	operator: 60 operands: 24
20	Operation	operator: 25 operand: 31
21	ExprTuple	58
22	ExprTuple	27
23	Conditional	value: 28 condition: 29
24	ExprTuple	59, 30
25	Literal
26	ExprTuple	31
27	ExprRange	lambda_map: 57 start_index: 58 end_index: 32
28	Operation	operator: 60 operands: 33
29	Operation	operator: 44 operands: 34
30	Literal
31	Lambda	parameters: 51 body: 35
32	Operation	operator: 53 operands: 36
33	ExprTuple	37, 63
34	ExprTuple	38
35	Conditional	value: 39 condition: 40
36	ExprTuple	59, 41
37	Operation	operator: 50 operands: 42
38	ExprRange	lambda_map: 52 start_index: 58 end_index: 49
39	Operation	operator: 60 operands: 43
40	Operation	operator: 44 operands: 45
41	Literal
42	ExprTuple	46
43	ExprTuple	47, 63
44	Literal
45	ExprTuple	48
46	ExprRange	lambda_map: 57 start_index: 58 end_index: 49
47	Operation	operator: 50 operands: 51
48	ExprRange	lambda_map: 52 start_index: 58 end_index: 59
49	Operation	operator: 53 operands: 54
50	Literal
51	ExprTuple	55
52	Lambda	parameter: 66 body: 56
53	Literal
54	ExprTuple	59, 58
55	ExprRange	lambda_map: 57 start_index: 58 end_index: 59
56	Operation	operator: 60 operands: 61
57	Lambda	parameter: 66 body: 62
58	Literal
59	Variable
60	Literal
61	ExprTuple	62, 63
62	IndexedVar	variable: 64 index: 66
63	Literal
64	Variable
65	ExprTuple	66
66	Variable