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 = InSet(B, Boolean), condition = InSet(Or(A_1_to_m, B, C_1_to_n), Boolean)), 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}~|~\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) \in \mathbb{B}}~\left(B \in \mathbb{B}\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: 7
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7
5	Literal
6	ExprTuple	8, 9
7	Lambda	parameters: 22 body: 10
8	Operation	operator: 17 operands: 11
9	Operation	operator: 17 operands: 12
10	Conditional	value: 13 condition: 14
11	ExprTuple	27, 15
12	ExprTuple	30, 15
13	Operation	operator: 17 operands: 16
14	Operation	operator: 17 operands: 18
15	Literal
16	ExprTuple	24, 20
17	Literal
18	ExprTuple	19, 20
19	Operation	operator: 21 operands: 22
20	Literal
21	Literal
22	ExprTuple	23, 24, 25
23	ExprRange	lambda_map: 26 start_index: 29 end_index: 27
24	Variable
25	ExprRange	lambda_map: 28 start_index: 29 end_index: 30
26	Lambda	parameter: 36 body: 31
27	Variable
28	Lambda	parameter: 36 body: 32
29	Literal
30	Variable
31	IndexedVar	variable: 33 index: 36
32	IndexedVar	variable: 34 index: 36
33	Variable
34	Variable
35	ExprTuple	36
36	Variable