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 A, Conditional, ExprRange, IndexedVar, Variable, m
from proveit.core_expr_types import A_1_to_m
from proveit.logic import And, Forall, InSet, Not, Or
from proveit.numbers import Natural, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Conditional(Forall(instance_param_or_params = [A_1_to_m], instance_expr = And(A_1_to_m), condition = Not(Or(ExprRange(sub_expr1, Not(IndexedVar(A, sub_expr1)), one, m)))), InSet(m, 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}~|~\lnot \left((\lnot A_{1}) \lor  (\lnot A_{2}) \lor  \ldots \lor  (\lnot A_{m})\right)}~\left(A_{1} \land  A_{2} \land  \ldots \land  A_{m}\right) \textrm{ if } m \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	23, 8
7	Lambda	parameters: 13 body: 9
8	Literal
9	Conditional	value: 10 condition: 11
10	Operation	operator: 12 operands: 13
11	Operation	operator: 25 operand: 16
12	Literal
13	ExprTuple	15
14	ExprTuple	16
15	ExprRange	lambda_map: 17 start_index: 22 end_index: 23
16	Operation	operator: 18 operands: 19
17	Lambda	parameter: 30 body: 27
18	Literal
19	ExprTuple	20
20	ExprRange	lambda_map: 21 start_index: 22 end_index: 23
21	Lambda	parameter: 30 body: 24
22	Literal
23	Variable
24	Operation	operator: 25 operand: 27
25	Literal
26	ExprTuple	27
27	IndexedVar	variable: 28 index: 30
28	Variable
29	ExprTuple	30
30	Variable