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, Lambda, n
from proveit.core_expr_types import a_1_to_n
from proveit.logic import Forall, InSet, NotEquals
from proveit.numbers import ComplexNonZero, Mult, Natural, zero

# build up the expression from sub-expressions
expr = Lambda(n, Conditional(Forall(instance_param_or_params = [a_1_to_n], instance_expr = NotEquals(Mult(a_1_to_n), zero), domain = ComplexNonZero), 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}^{\neq 0}}~\left(\left(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{n}\right) \neq 0\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: 27 body: 2
1	ExprTuple	27
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 8
4	Operation	operator: 28 operands: 7
5	Literal
6	ExprTuple	8
7	ExprTuple	27, 9
8	Lambda	parameters: 21 body: 10
9	Literal
10	Conditional	value: 11 condition: 12
11	Operation	operator: 13 operands: 14
12	Operation	operator: 15 operands: 16
13	Literal
14	ExprTuple	17, 18
15	Literal
16	ExprTuple	19
17	Operation	operator: 20 operands: 21
18	Literal
19	ExprRange	lambda_map: 22 start_index: 26 end_index: 27
20	Literal
21	ExprTuple	23
22	Lambda	parameter: 34 body: 24
23	ExprRange	lambda_map: 25 start_index: 26 end_index: 27
24	Operation	operator: 28 operands: 29
25	Lambda	parameter: 34 body: 30
26	Literal
27	Variable
28	Literal
29	ExprTuple	30, 31
30	IndexedVar	variable: 32 index: 34
31	Literal
32	Variable
33	ExprTuple	34
34	Variable