Expression of type Lambda

from the theory of proveit.numbers.summation

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, IndexedVar, Lambda, Variable, a, c, l
from proveit.logic import InSet
from proveit.numbers import Add, Integer, Mult, one, zero

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Lambda(l, Conditional(Mult(ExprRange(sub_expr1, IndexedVar(a, sub_expr1), one, zero), Add(l, one), IndexedVar(c, one)), InSet(l, Integer)))

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())

l \mapsto \left\{a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{0} \cdot \left(l + 1\right) \cdot c_{1} \textrm{ if } l \in \mathbb{Z}\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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