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, Or
from proveit.numbers import Natural, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
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(B_1_to_m), domain = Boolean, conditions = [Or(A_1_to_m), ExprRange(sub_expr1, Implies(IndexedVar(A, sub_expr1), IndexedVar(B, sub_expr1)), 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}~|~A_{1} \lor  A_{2} \lor  \ldots \lor  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(B_{1} \lor  B_{2} \lor  \ldots \lor  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: 39 body: 4
3	ExprTuple	39
4	Conditional	value: 5 condition: 6
5	Operation	operator: 7 operand: 10
6	Operation	operator: 35 operands: 9
7	Literal
8	ExprTuple	10
9	ExprTuple	39, 11
10	Lambda	parameters: 12 body: 13
11	Literal
12	ExprTuple	32, 19
13	Conditional	value: 14 condition: 15
14	Operation	operator: 27 operands: 16
15	Operation	operator: 17 operands: 18
16	ExprTuple	19
17	Literal
18	ExprTuple	20, 21, 22, 23
19	ExprRange	lambda_map: 24 start_index: 38 end_index: 39
20	ExprRange	lambda_map: 25 start_index: 38 end_index: 39
21	ExprRange	lambda_map: 26 start_index: 38 end_index: 39
22	Operation	operator: 27 operands: 28
23	ExprRange	lambda_map: 29 start_index: 38 end_index: 39
24	Lambda	parameter: 48 body: 44
25	Lambda	parameter: 48 body: 30
26	Lambda	parameter: 48 body: 31
27	Literal
28	ExprTuple	32
29	Lambda	parameter: 48 body: 33
30	Operation	operator: 35 operands: 34
31	Operation	operator: 35 operands: 36
32	ExprRange	lambda_map: 37 start_index: 38 end_index: 39
33	Operation	operator: 40 operands: 41
34	ExprTuple	43, 42
35	Literal
36	ExprTuple	44, 42
37	Lambda	parameter: 48 body: 43
38	Literal
39	Variable
40	Literal
41	ExprTuple	43, 44
42	Literal
43	IndexedVar	variable: 45 index: 48
44	IndexedVar	variable: 46 index: 48
45	Variable
46	Variable
47	ExprTuple	48
48	Variable