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, IndexedVar, Lambda, Variable, a, n
from proveit.core_expr_types import a_1_to_n
from proveit.logic import Equals, Forall, InSet, Or
from proveit.numbers import Complex, Mult, Natural, ZeroSet, one, zero

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Lambda(n, Conditional(Forall(instance_param_or_params = [a_1_to_n], instance_expr = InSet(Mult(a_1_to_n), ZeroSet), domain = Complex, condition = Or(ExprRange(sub_expr1, Equals(IndexedVar(a, sub_expr1), zero), one, n))), InSet(n, Natural)))

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())

n \mapsto \left\{\forall_{a_{1}, a_{2}, \ldots, a_{n} \in \mathbb{C}~|~\left(a_{1} = 0\right) \lor  \left(a_{2} = 0\right) \lor  \ldots \lor  \left(a_{n} = 0\right)}~\left(\left(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{n}\right) \in \left\{0\right\}\right) \textrm{ if } n \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: 35 body: 2
1	ExprTuple	35
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 8
4	Operation	operator: 31 operands: 7
5	Literal
6	ExprTuple	8
7	ExprTuple	35, 9
8	Lambda	parameters: 21 body: 10
9	Literal
10	Conditional	value: 11 condition: 12
11	Operation	operator: 31 operands: 13
12	Operation	operator: 14 operands: 15
13	ExprTuple	16, 17
14	Literal
15	ExprTuple	18, 19
16	Operation	operator: 20 operands: 21
17	Operation	operator: 22 operand: 41
18	ExprRange	lambda_map: 24 start_index: 34 end_index: 35
19	Operation	operator: 25 operands: 26
20	Literal
21	ExprTuple	27
22	Literal
23	ExprTuple	41
24	Lambda	parameter: 44 body: 28
25	Literal
26	ExprTuple	29
27	ExprRange	lambda_map: 30 start_index: 34 end_index: 35
28	Operation	operator: 31 operands: 32
29	ExprRange	lambda_map: 33 start_index: 34 end_index: 35
30	Lambda	parameter: 44 body: 40
31	Literal
32	ExprTuple	40, 36
33	Lambda	parameter: 44 body: 37
34	Literal
35	Variable
36	Literal
37	Operation	operator: 38 operands: 39
38	Literal
39	ExprTuple	40, 41
40	IndexedVar	variable: 42 index: 44
41	Literal
42	Variable
43	ExprTuple	44
44	Variable