Expression of type Forall

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 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, sub_expr1)
sub_expr3 = Add(m, one)
expr = Forall(instance_param_or_params = [m], instance_expr = Forall(instance_param_or_params = [ExprRange(sub_expr1, sub_expr2, one, Add(m, two))], instance_expr = InSet(Or(ExprRange(sub_expr1, sub_expr2, one, sub_expr3)), Boolean), condition = ExprRange(sub_expr1, InSet(sub_expr2, Boolean), one, sub_expr3)), 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())

\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]

stored_expr.style_options()

name	description	default	current value	related methods
with_wrapping	If 'True', wrap the Expression after the parameters	None	None/False	('with_wrapping',)
condition_wrapping	Wrap 'before' or 'after' the condition (or None).	None	None/False	('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_params	If 'True', wraps every two parameters AND wraps the Expression after the parameters	None	None/False	('with_params',)
justification	justify to the 'left', 'center', or 'right' in the array cells	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

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