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 C, l, m, n
from proveit.core_expr_types import A_1_to_l, B_1_to_m, D_1_to_n
from proveit.logic import Forall, Or
from proveit.numbers import Natural

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [l, m, n], instance_expr = Forall(instance_param_or_params = [A_1_to_l, B_1_to_m, C, D_1_to_n], instance_expr = Or(A_1_to_l, C, B_1_to_m, D_1_to_n), condition = Or(A_1_to_l, B_1_to_m, C, D_1_to_n)), 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_{l, m, n \in \mathbb{N}}~\left[\forall_{A_{1}, A_{2}, \ldots, A_{l}, B_{1}, B_{2}, \ldots, B_{m}, C, D_{1}, D_{2}, \ldots, D_{n}~|~A_{1} \lor  A_{2} \lor  \ldots \lor  A_{l}\lor B_{1} \lor  B_{2} \lor  \ldots \lor  B_{m} \lor C\lor D_{1} \lor  D_{2} \lor  \ldots \lor  D_{n}}~\left(A_{1} \lor  A_{2} \lor  \ldots \lor  A_{l} \lor C\lor B_{1} \lor  B_{2} \lor  \ldots \lor  B_{m}\lor D_{1} \lor  D_{2} \lor  \ldots \lor  D_{n}\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	parameters: 3 body: 4
3	ExprTuple	31, 33, 36
4	Conditional	value: 5 condition: 6
5	Operation	operator: 7 operand: 11
6	Operation	operator: 9 operands: 10
7	Literal
8	ExprTuple	11
9	Literal
10	ExprTuple	12, 13, 14
11	Lambda	parameters: 25 body: 15
12	Operation	operator: 18 operands: 16
13	Operation	operator: 18 operands: 17
14	Operation	operator: 18 operands: 19
15	Conditional	value: 20 condition: 21
16	ExprTuple	31, 22
17	ExprTuple	33, 22
18	Literal
19	ExprTuple	36, 22
20	Operation	operator: 24 operands: 23
21	Operation	operator: 24 operands: 25
22	Literal
23	ExprTuple	26, 28, 27, 29
24	Literal
25	ExprTuple	26, 27, 28, 29
26	ExprRange	lambda_map: 30 start_index: 35 end_index: 31
27	ExprRange	lambda_map: 32 start_index: 35 end_index: 33
28	Variable
29	ExprRange	lambda_map: 34 start_index: 35 end_index: 36
30	Lambda	parameter: 44 body: 37
31	Variable
32	Lambda	parameter: 44 body: 38
33	Variable
34	Lambda	parameter: 44 body: 39
35	Literal
36	Variable
37	IndexedVar	variable: 40 index: 44
38	IndexedVar	variable: 41 index: 44
39	IndexedVar	variable: 42 index: 44
40	Variable
41	Variable
42	Variable
43	ExprTuple	44
44	Variable