Expression of type Conditional

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 Conditional, l, m, n
from proveit.core_expr_types import A_1_to_l, B_1_to_m, C_1_to_n
from proveit.logic import And, Forall, InSet, Or
from proveit.numbers import Natural

# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [A_1_to_l, B_1_to_m, C_1_to_n], instance_expr = Or(A_1_to_l, B_1_to_m, C_1_to_n), condition = Or(A_1_to_l, Or(B_1_to_m), C_1_to_n)), And(InSet(l, Natural), InSet(m, Natural), InSet(n, 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())

\left\{\forall_{A_{1}, A_{2}, \ldots, A_{l}, B_{1}, B_{2}, \ldots, B_{m}, C_{1}, C_{2}, \ldots, C_{n}~|~A_{1} \lor  A_{2} \lor  \ldots \lor  A_{l} \lor \left(B_{1} \lor  B_{2} \lor  \ldots \lor  B_{m}\right)\lor C_{1} \lor  C_{2} \lor  \ldots \lor  C_{n}}~\left(A_{1} \lor  A_{2} \lor  \ldots \lor  A_{l}\lor B_{1} \lor  B_{2} \lor  \ldots \lor  B_{m}\lor C_{1} \lor  C_{2} \lor  \ldots \lor  C_{n}\right) \textrm{ if } l \in \mathbb{N} ,  m \in \mathbb{N} ,  n \in \mathbb{N}\right..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

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