Expression of type Lambda

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 ExprRange, Lambda, S, Variable, m
from proveit.logic import CartExp, CartProd, Equals
from proveit.numbers import one

# 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:

# 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())

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

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 16 body: 2
1	ExprTuple	16
2	Operation	operator: 3 operands: 4
3	Literal
4	ExprTuple	5, 6
5	Operation	operator: 7 operands: 8
6	Operation	operator: 9 operands: 10
7	Literal
8	ExprTuple	16, 14
9	Literal
10	ExprTuple	11
11	ExprRange	lambda_map: 12 start_index: 13 end_index: 14
12	Lambda	parameter: 17 body: 16
13	Literal
14	Variable
15	ExprTuple	17
16	Variable
17	Variable