Expression of type Conditional

from the theory of proveit.logic.booleans.conjunction

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, m, n
from proveit.core_expr_types import A_1_to_m, C_1_to_n
from proveit.logic import And, Boolean, Equals, FALSE, Forall, InSet
from proveit.numbers import Natural

# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [A_1_to_m, C_1_to_n], instance_expr = Equals(And(A_1_to_m, FALSE, C_1_to_n), FALSE), domain = 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}, C_{1}, C_{2}, \ldots, C_{n} \in \mathbb{B}}~\left(\left(A_{1} \land  A_{2} \land  \ldots \land  A_{m} \land \bot\land C_{1} \land  C_{2} \land  \ldots \land  C_{n}\right) = \bot\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: 22 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	7, 8
6	Lambda	parameters: 9 body: 10
7	Operation	operator: 37 operands: 11
8	Operation	operator: 37 operands: 12
9	ExprTuple	26, 28
10	Conditional	value: 13 condition: 14
11	ExprTuple	32, 15
12	ExprTuple	35, 15
13	Operation	operator: 16 operands: 17
14	Operation	operator: 22 operands: 18
15	Literal
16	Literal
17	ExprTuple	19, 27
18	ExprTuple	20, 21
19	Operation	operator: 22 operands: 23
20	ExprRange	lambda_map: 24 start_index: 34 end_index: 32
21	ExprRange	lambda_map: 25 start_index: 34 end_index: 35
22	Literal
23	ExprTuple	26, 27, 28
24	Lambda	parameter: 45 body: 29
25	Lambda	parameter: 45 body: 30
26	ExprRange	lambda_map: 31 start_index: 34 end_index: 32
27	Literal
28	ExprRange	lambda_map: 33 start_index: 34 end_index: 35
29	Operation	operator: 37 operands: 36
30	Operation	operator: 37 operands: 38
31	Lambda	parameter: 45 body: 39
32	Variable
33	Lambda	parameter: 45 body: 40
34	Literal
35	Variable
36	ExprTuple	39, 41
37	Literal
38	ExprTuple	40, 41
39	IndexedVar	variable: 42 index: 45
40	IndexedVar	variable: 43 index: 45
41	Literal
42	Variable
43	Variable
44	ExprTuple	45
45	Variable