Theorem eigen_exp_application of type Forall

from the theory of proveit.linear_algebra.matrices.exponentiation

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.exponentiation import eigen_exp_application

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

Passed sanity check: eigen_exp_application matches stored_expr

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

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