Expression of type Lambda

from the theory of proveit.linear_algebra.matrices.exponentiation

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 A, Conditional, Lambda, b, m, x
from proveit.linear_algebra import MatrixExp, MatrixMult, ScalarMult
from proveit.logic import Equals, Forall, InSet
from proveit.numbers import Complex, Exp, NaturalPos

# build up the expression from sub-expressions
expr = Lambda(m, Conditional(Forall(instance_param_or_params = [b], instance_expr = Forall(instance_param_or_params = [A, x], instance_expr = Equals(MatrixMult(MatrixExp(A, m), x), MatrixMult(Exp(b, m), x)), condition = Equals(MatrixMult(A, x), ScalarMult(b, x))), domain = Complex), InSet(m, NaturalPos)))

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())

m \mapsto \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] \textrm{ if } m \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: 44 body: 2
1	ExprTuple	44
2	Conditional	value: 3 condition: 4
3	Operation	operator: 13 operand: 7
4	Operation	operator: 15 operands: 6
5	ExprTuple	7
6	ExprTuple	44, 8
7	Lambda	parameter: 43 body: 10
8	Literal
9	ExprTuple	43
10	Conditional	value: 11 condition: 12
11	Operation	operator: 13 operand: 17
12	Operation	operator: 15 operands: 16
13	Literal
14	ExprTuple	17
15	Literal
16	ExprTuple	43, 18
17	Lambda	parameters: 32 body: 19
18	Literal
19	Conditional	value: 20 condition: 21
20	Operation	operator: 23 operands: 22
21	Operation	operator: 23 operands: 24
22	ExprTuple	25, 26
23	Literal
24	ExprTuple	27, 28
25	Operation	operator: 31 operands: 29
26	Operation	operator: 31 operands: 30
27	Operation	operator: 31 operands: 32
28	Operation	operator: 33 operands: 34
29	ExprTuple	35, 37
30	ExprTuple	36, 37
31	Literal
32	ExprTuple	42, 37
33	Literal
34	ExprTuple	43, 37
35	Operation	operator: 38 operands: 39
36	Operation	operator: 40 operands: 41
37	Variable
38	Literal
39	ExprTuple	42, 44
40	Literal
41	ExprTuple	43, 44
42	Variable
43	Variable
44	Variable