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 B, Conditional, m, n
from proveit.core_expr_types import A_1_to_m, C_1_to_n
from proveit.logic import And, Boolean, 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_m, B, C_1_to_n], instance_expr = Or(A_1_to_m, B, C_1_to_n), domain = Boolean, condition = B), And(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_{m}, B, C_{1}, C_{2}, \ldots, C_{n} \in \mathbb{B}~|~B}~\left(A_{1} \lor  A_{2} \lor  \ldots \lor  A_{m} \lor B\lor C_{1} \lor  C_{2} \lor  \ldots \lor  C_{n}\right) \textrm{ if } 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: 6
2	Operation	operator: 17 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	7, 8
6	Lambda	parameters: 16 body: 9
7	Operation	operator: 36 operands: 10
8	Operation	operator: 36 operands: 11
9	Conditional	value: 12 condition: 13
10	ExprTuple	27, 14
11	ExprTuple	31, 14
12	Operation	operator: 15 operands: 16
13	Operation	operator: 17 operands: 18
14	Literal
15	Literal
16	ExprTuple	19, 33, 20
17	Literal
18	ExprTuple	21, 22, 23, 33
19	ExprRange	lambda_map: 24 start_index: 30 end_index: 27
20	ExprRange	lambda_map: 25 start_index: 30 end_index: 31
21	ExprRange	lambda_map: 26 start_index: 30 end_index: 27
22	Operation	operator: 36 operands: 28
23	ExprRange	lambda_map: 29 start_index: 30 end_index: 31
24	Lambda	parameter: 44 body: 38
25	Lambda	parameter: 44 body: 39
26	Lambda	parameter: 44 body: 32
27	Variable
28	ExprTuple	33, 40
29	Lambda	parameter: 44 body: 34
30	Literal
31	Variable
32	Operation	operator: 36 operands: 35
33	Variable
34	Operation	operator: 36 operands: 37
35	ExprTuple	38, 40
36	Literal
37	ExprTuple	39, 40
38	IndexedVar	variable: 41 index: 44
39	IndexedVar	variable: 42 index: 44
40	Literal
41	Variable
42	Variable
43	ExprTuple	44
44	Variable