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 Conditional, ExprRange, Lambda, 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 = Lambda(m, 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())

m \mapsto \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()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 24 body: 2
1	ExprTuple	24
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 9
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9
7	Literal
8	ExprTuple	24, 10
9	Lambda	parameter: 26 body: 12
10	Literal
11	ExprTuple	26
12	Operation	operator: 13 operands: 14
13	Literal
14	ExprTuple	15, 16
15	Operation	operator: 17 operands: 18
16	Operation	operator: 19 operands: 20
17	Literal
18	ExprTuple	26, 24
19	Literal
20	ExprTuple	21
21	ExprRange	lambda_map: 22 start_index: 23 end_index: 24
22	Lambda	parameter: 27 body: 26
23	Literal
24	Variable
25	ExprTuple	27
26	Variable
27	Variable