Expression of type ExprTuple

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, ExprTuple, 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 = ExprTuple(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())

\left(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..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameter: 45 body: 3
2	ExprTuple	45
3	Conditional	value: 4 condition: 5
4	Operation	operator: 14 operand: 8
5	Operation	operator: 16 operands: 7
6	ExprTuple	8
7	ExprTuple	45, 9
8	Lambda	parameter: 44 body: 11
9	Literal
10	ExprTuple	44
11	Conditional	value: 12 condition: 13
12	Operation	operator: 14 operand: 18
13	Operation	operator: 16 operands: 17
14	Literal
15	ExprTuple	18
16	Literal
17	ExprTuple	44, 19
18	Lambda	parameters: 33 body: 20
19	Literal
20	Conditional	value: 21 condition: 22
21	Operation	operator: 24 operands: 23
22	Operation	operator: 24 operands: 25
23	ExprTuple	26, 27
24	Literal
25	ExprTuple	28, 29
26	Operation	operator: 32 operands: 30
27	Operation	operator: 32 operands: 31
28	Operation	operator: 32 operands: 33
29	Operation	operator: 34 operands: 35
30	ExprTuple	36, 38
31	ExprTuple	37, 38
32	Literal
33	ExprTuple	43, 38
34	Literal
35	ExprTuple	44, 38
36	Operation	operator: 39 operands: 40
37	Operation	operator: 41 operands: 42
38	Variable
39	Literal
40	ExprTuple	43, 45
41	Literal
42	ExprTuple	44, 45
43	Variable
44	Variable
45	Variable