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 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 = [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)])

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_{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)

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