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 And, Equals, InSet, Or
from proveit.numbers import Complex, Mult, ZeroSet, one, zero

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = IndexedVar(a, sub_expr1)
expr = Lambda([a_1_to_n], Conditional(InSet(Mult(a_1_to_n), ZeroSet), And(ExprRange(sub_expr1, InSet(sub_expr2, Complex), one, n), Or(ExprRange(sub_expr1, Equals(sub_expr2, zero), one, n)))))

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(a_{1}, a_{2}, \ldots, a_{n}\right) \mapsto \left\{\left(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{n}\right) \in \left\{0\right\} \textrm{ if } \left(a_{1} \in \mathbb{C}\right) ,  \left(a_{2} \in \mathbb{C}\right) ,  \ldots ,  \left(a_{n} \in \mathbb{C}\right) ,  \left(a_{1} = 0\right) \lor  \left(a_{2} = 0\right) \lor  \ldots \lor  \left(a_{n} = 0\right)\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 12 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 22 operands: 4
3	Operation	operator: 5 operands: 6
4	ExprTuple	7, 8
5	Literal
6	ExprTuple	9, 10
7	Operation	operator: 11 operands: 12
8	Operation	operator: 13 operand: 32
9	ExprRange	lambda_map: 15 start_index: 25 end_index: 26
10	Operation	operator: 16 operands: 17
11	Literal
12	ExprTuple	18
13	Literal
14	ExprTuple	32
15	Lambda	parameter: 35 body: 19
16	Literal
17	ExprTuple	20
18	ExprRange	lambda_map: 21 start_index: 25 end_index: 26
19	Operation	operator: 22 operands: 23
20	ExprRange	lambda_map: 24 start_index: 25 end_index: 26
21	Lambda	parameter: 35 body: 31
22	Literal
23	ExprTuple	31, 27
24	Lambda	parameter: 35 body: 28
25	Literal
26	Variable
27	Literal
28	Operation	operator: 29 operands: 30
29	Literal
30	ExprTuple	31, 32
31	IndexedVar	variable: 33 index: 35
32	Literal
33	Variable
34	ExprTuple	35
35	Variable