Expression of type And

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, IndexedVar, Variable, m
from proveit.core_expr_types import A_1_to_m
from proveit.logic import And, 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 = And(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)\right] \land \left[\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
operation	'infix' or 'function' style formatting	infix	infix
wrap_positions	position(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.	()	()	('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 45 operands: 1
1	ExprTuple	2, 3
2	Operation	operator: 26 operand: 6
3	Operation	operator: 26 operand: 7
4	ExprTuple	6
5	ExprTuple	7
6	Lambda	parameter: 18 body: 9
7	Lambda	parameter: 60 body: 11
8	ExprTuple	18
9	Conditional	value: 12 condition: 12
10	ExprTuple	60
11	Conditional	value: 13 condition: 14
12	Operation	operator: 61 operands: 15
13	Operation	operator: 26 operand: 19
14	Operation	operator: 45 operands: 17
15	ExprTuple	18, 64
16	ExprTuple	19
17	ExprTuple	20, 21
18	IndexedVar	variable: 65 index: 59
19	Lambda	parameters: 23 body: 24
20	Operation	operator: 61 operands: 25
21	Operation	operator: 26 operand: 32
22	ExprTuple	59
23	ExprTuple	28
24	Conditional	value: 29 condition: 30
25	ExprTuple	60, 31
26	Literal
27	ExprTuple	32
28	ExprRange	lambda_map: 58 start_index: 59 end_index: 33
29	Operation	operator: 61 operands: 34
30	Operation	operator: 45 operands: 35
31	Literal
32	Lambda	parameters: 52 body: 36
33	Operation	operator: 54 operands: 37
34	ExprTuple	38, 64
35	ExprTuple	39
36	Conditional	value: 40 condition: 41
37	ExprTuple	60, 42
38	Operation	operator: 51 operands: 43
39	ExprRange	lambda_map: 53 start_index: 59 end_index: 50
40	Operation	operator: 61 operands: 44
41	Operation	operator: 45 operands: 46
42	Literal
43	ExprTuple	47
44	ExprTuple	48, 64
45	Literal
46	ExprTuple	49
47	ExprRange	lambda_map: 58 start_index: 59 end_index: 50
48	Operation	operator: 51 operands: 52
49	ExprRange	lambda_map: 53 start_index: 59 end_index: 60
50	Operation	operator: 54 operands: 55
51	Literal
52	ExprTuple	56
53	Lambda	parameter: 67 body: 57
54	Literal
55	ExprTuple	60, 59
56	ExprRange	lambda_map: 58 start_index: 59 end_index: 60
57	Operation	operator: 61 operands: 62
58	Lambda	parameter: 67 body: 63
59	Literal
60	Variable
61	Literal
62	ExprTuple	63, 64
63	IndexedVar	variable: 65 index: 67
64	Literal
65	Variable
66	ExprTuple	67
67	Variable