# from the theory of proveit.logic.sets.cartesian_products¶

In [1]:
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 ExprRange, Lambda, S, Variable, m
from proveit.logic import CartExp, CartProd, Equals
from proveit.numbers import one

In [2]:
# build up the expression from sub-expressions
expr = Lambda(S, Equals(CartExp(S, m), CartProd(ExprRange(Variable("_a", latex_format = r"{_{-}a}"), S, one, m))))

expr:
In [3]:
# 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

In [4]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

S \mapsto \left(S^{m} = \left(S \times  S \times  ..\left(m - 3\right) \times.. \times  S\right)\right)

In [5]:
stored_expr.style_options()

no style options
In [6]:
# display the expression information
stored_expr.expr_info()

core typesub-expressionsexpression
0Lambdaparameter: 16
body: 2
1ExprTuple16
2Operationoperator: 3
operands: 4
3Literal
4ExprTuple5, 6
5Operationoperator: 7
operands: 8
6Operationoperator: 9
operands: 10
7Literal
8ExprTuple16, 14
9Literal
10ExprTuple11
11ExprRangelambda_map: 12
start_index: 13
end_index: 14
12Lambdaparameter: 17
body: 16
13Literal
14Variable
15ExprTuple17
16Variable
17Variable