Theorem mult_not_eq_zero of type Forall

from the theory of proveit.numbers.multiplication

see dependencies

import proveit
# Automation is not needed when only building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_theorem_expr # Load the stored theorem expression as 'stored_expr'
# import the special expression
from proveit.numbers.multiplication import mult_not_eq_zero

# check that the built expression is the same as the stored expression
assert mult_not_eq_zero.expr == stored_expr
assert mult_not_eq_zero.expr._style_id == stored_expr._style_id
print("Passed sanity check: mult_not_eq_zero matches stored_expr")

Passed sanity check: mult_not_eq_zero matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\forall_{n \in \mathbb{N}}~\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)\right]

stored_expr.style_options()

name	description	default	current value	related methods
with_wrapping	If 'True', wrap the Expression after the parameters	None	None/False	('with_wrapping',)
condition_wrapping	Wrap 'before' or 'after' the condition (or None).	None	None/False	('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_params	If 'True', wraps every two parameters AND wraps the Expression after the parameters	None	None/False	('with_params',)
justification	justify to the 'left', 'center', or 'right' in the array cells	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 7 operand: 2
1	ExprTuple	2
2	Lambda	parameter: 29 body: 4
3	ExprTuple	29
4	Conditional	value: 5 condition: 6
5	Operation	operator: 7 operand: 10
6	Operation	operator: 30 operands: 9
7	Literal
8	ExprTuple	10
9	ExprTuple	29, 11
10	Lambda	parameters: 23 body: 12
11	Literal
12	Conditional	value: 13 condition: 14
13	Operation	operator: 15 operands: 16
14	Operation	operator: 17 operands: 18
15	Literal
16	ExprTuple	19, 20
17	Literal
18	ExprTuple	21
19	Operation	operator: 22 operands: 23
20	Literal
21	ExprRange	lambda_map: 24 start_index: 28 end_index: 29
22	Literal
23	ExprTuple	25
24	Lambda	parameter: 36 body: 26
25	ExprRange	lambda_map: 27 start_index: 28 end_index: 29
26	Operation	operator: 30 operands: 31
27	Lambda	parameter: 36 body: 32
28	Literal
29	Variable
30	Literal
31	ExprTuple	32, 33
32	IndexedVar	variable: 34 index: 36
33	Literal
34	Variable
35	ExprTuple	36
36	Variable