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, B, ExprRange, IndexedVar, Variable, m
from proveit.core_expr_types import A_1_to_m, B_1_to_m
from proveit.logic import Boolean, Forall, Implies, Not, Or
from proveit.numbers import Natural, 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 = Forall(instance_param_or_params = [m], instance_expr = Forall(instance_param_or_params = [A_1_to_m, B_1_to_m], instance_expr = Or(ExprRange(sub_expr1, Not(sub_expr2), one, m)), domain = Boolean, conditions = [Or(ExprRange(sub_expr1, Not(sub_expr3), one, m)), ExprRange(sub_expr1, Implies(sub_expr3, sub_expr2), one, m)]), domain = Natural)

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