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 B, Conditional, m, n
from proveit.core_expr_types import A_1_to_m, C_1_to_n
from proveit.logic import And, Forall, InSet, Not
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 = Not(And(A_1_to_m, B, C_1_to_n)), condition = Not(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}~|~\lnot B}~(\lnot \left(A_{1} \land  A_{2} \land  \ldots \land  A_{m} \land B\land C_{1} \land  C_{2} \land  \ldots \land  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: 20 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	7, 8
6	Lambda	parameters: 21 body: 9
7	Operation	operator: 11 operands: 10
8	Operation	operator: 11 operands: 12
9	Conditional	value: 13 condition: 14
10	ExprTuple	26, 15
11	Literal
12	ExprTuple	29, 15
13	Operation	operator: 17 operand: 19
14	Operation	operator: 17 operand: 23
15	Literal
16	ExprTuple	19
17	Literal
18	ExprTuple	23
19	Operation	operator: 20 operands: 21
20	Literal
21	ExprTuple	22, 23, 24
22	ExprRange	lambda_map: 25 start_index: 28 end_index: 26
23	Variable
24	ExprRange	lambda_map: 27 start_index: 28 end_index: 29
25	Lambda	parameter: 35 body: 30
26	Variable
27	Lambda	parameter: 35 body: 31
28	Literal
29	Variable
30	IndexedVar	variable: 32 index: 35
31	IndexedVar	variable: 33 index: 35
32	Variable
33	Variable
34	ExprTuple	35
35	Variable