Theorem eigen_pow of type Forall

from the theory of proveit.linear_algebra.matrices

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.linear_algebra.matrices import eigen_pow

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

Passed sanity check: eigen_pow matches stored_expr

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

\forall_{k \in \mathbb{N}^+}~\left[\forall_{b \in \mathbb{C}}~\left[\forall_{A, x}~\left(\left(\left(A \thinspace x\right) = \left(b \cdot x\right)\right) \Rightarrow \left(\left(A^{k} \thinspace x\right) = \left(b^{k} \cdot x\right)\right)\right)\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: 15 operand: 2
1	ExprTuple	2
2	Lambda	parameter: 47 body: 4
3	ExprTuple	47
4	Conditional	value: 5 condition: 6
5	Operation	operator: 15 operand: 9
6	Operation	operator: 17 operands: 8
7	ExprTuple	9
8	ExprTuple	47, 10
9	Lambda	parameter: 46 body: 12
10	Literal
11	ExprTuple	46
12	Conditional	value: 13 condition: 14
13	Operation	operator: 15 operand: 19
14	Operation	operator: 17 operands: 18
15	Literal
16	ExprTuple	19
17	Literal
18	ExprTuple	46, 20
19	Lambda	parameters: 33 body: 21
20	Literal
21	Operation	operator: 22 operands: 23
22	Literal
23	ExprTuple	24, 25
24	Operation	operator: 27 operands: 26
25	Operation	operator: 27 operands: 28
26	ExprTuple	29, 30
27	Literal
28	ExprTuple	31, 32
29	Operation	operator: 35 operands: 33
30	Operation	operator: 37 operands: 34
31	Operation	operator: 35 operands: 36
32	Operation	operator: 37 operands: 38
33	ExprTuple	45, 41
34	ExprTuple	46, 41
35	Literal
36	ExprTuple	39, 41
37	Literal
38	ExprTuple	40, 41
39	Operation	operator: 43 operands: 42
40	Operation	operator: 43 operands: 44
41	Variable
42	ExprTuple	45, 47
43	Literal
44	ExprTuple	46, 47
45	Variable
46	Variable
47	Variable