Expression of type Lambda

from the theory of proveit.numbers.multiplication

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, Variable, n, x
from proveit.logic import And, Equals, InSet
from proveit.numbers import Add, Complex, Mult, Natural, one

# build up the expression from sub-expressions
expr = Lambda([n, x], Conditional(Equals(Add(ExprRange(Variable("_a", latex_format = r"{_{-}a}"), x, one, n)), Mult(x, n)), And(InSet(n, Natural), InSet(x, Complex))))

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(n, x\right) \mapsto \left\{\left(x +  x +  ..\left(n - 3\right) \times.. +  x\right) = \left(x \cdot n\right) \textrm{ if } n \in \mathbb{N} ,  x \in \mathbb{C}\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 1 body: 2
1	ExprTuple	25, 27
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9, 10
7	Literal
8	ExprTuple	11, 12
9	Operation	operator: 13 operands: 14
10	Operation	operator: 15 operands: 16
11	Operation	operator: 18 operands: 17
12	Operation	operator: 18 operands: 19
13	Literal
14	ExprTuple	20
15	Literal
16	ExprTuple	27, 25
17	ExprTuple	25, 21
18	Literal
19	ExprTuple	27, 22
20	ExprRange	lambda_map: 23 start_index: 24 end_index: 25
21	Literal
22	Literal
23	Lambda	parameter: 28 body: 27
24	Literal
25	Variable
26	ExprTuple	28
27	Variable
28	Variable