Expression of type Conditional

from the theory of proveit.logic.sets.cartesian_products

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, ExprRange, S, Variable, m
from proveit.logic import CartExp, CartProd, Equals, Forall, InSet
from proveit.numbers import NaturalPos, one

# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [S], instance_expr = Equals(CartExp(S, m), CartProd(ExprRange(Variable("_a", latex_format = r"{_{-}a}"), S, one, m)))), InSet(m, NaturalPos))

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_{S}~\left(S^{m} = \left(S \times  S \times  ..\left(m - 3\right) \times.. \times  S\right)\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	22, 8
7	Lambda	parameter: 24 body: 10
8	Literal
9	ExprTuple	24
10	Operation	operator: 11 operands: 12
11	Literal
12	ExprTuple	13, 14
13	Operation	operator: 15 operands: 16
14	Operation	operator: 17 operands: 18
15	Literal
16	ExprTuple	24, 22
17	Literal
18	ExprTuple	19
19	ExprRange	lambda_map: 20 start_index: 21 end_index: 22
20	Lambda	parameter: 25 body: 24
21	Literal
22	Variable
23	ExprTuple	25
24	Variable
25	Variable