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, Variable, n
from proveit.logic import And, Forall, InSet
from proveit.numbers import Natural, one

# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [A], instance_expr = And(ExprRange(Variable("_a", latex_format = r"{_{-}a}"), A, one, n)), condition = A), 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~|~A}~\left(A \land  A \land  ..\left(n - 3\right) \times.. \land  A\right) \textrm{ if } 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	17, 8
7	Lambda	parameter: 19 body: 10
8	Literal
9	ExprTuple	19
10	Conditional	value: 11 condition: 19
11	Operation	operator: 12 operands: 13
12	Literal
13	ExprTuple	14
14	ExprRange	lambda_map: 15 start_index: 16 end_index: 17
15	Lambda	parameter: 20 body: 19
16	Literal
17	Variable
18	ExprTuple	20
19	Variable
20	Variable