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 A, B, C, Conditional
from proveit.logic import And, Boolean, Forall, Implies, InSet, Or

# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [C], instance_expr = C, conditions = [Implies(A, C), Implies(B, C)]), And(InSet(A, Boolean), InSet(B, Boolean), Or(A, B)))

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_{C~|~A \Rightarrow C, B \Rightarrow C}~C \textrm{ if } A \in \mathbb{B} ,  B \in \mathbb{B} ,  A \lor B\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: 19 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	7, 8, 9
6	Lambda	parameter: 28 body: 11
7	Operation	operator: 13 operands: 12
8	Operation	operator: 13 operands: 14
9	Operation	operator: 15 operands: 16
10	ExprTuple	28
11	Conditional	value: 28 condition: 17
12	ExprTuple	26, 18
13	Literal
14	ExprTuple	27, 18
15	Literal
16	ExprTuple	26, 27
17	Operation	operator: 19 operands: 20
18	Literal
19	Literal
20	ExprTuple	21, 22
21	Operation	operator: 24 operands: 23
22	Operation	operator: 24 operands: 25
23	ExprTuple	26, 28
24	Literal
25	ExprTuple	27, 28
26	Variable
27	Variable
28	Variable