Expression of type ExprTuple

from the theory of proveit.linear_algebra.matrices

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, k, x
from proveit.linear_algebra import MatrixMult, ScalarMult
from proveit.logic import Equals, Forall, Implies, InSet
from proveit.numbers import Complex, Exp, NaturalPos

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(k, Conditional(Forall(instance_param_or_params = [b], instance_expr = Forall(instance_param_or_params = [A, x], instance_expr = Implies(Equals(MatrixMult(A, x), ScalarMult(b, x)), Equals(MatrixMult(Exp(A, k), x), ScalarMult(Exp(b, k), x)))), domain = Complex), InSet(k, 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(k \mapsto \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] \textrm{ if } k \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: 46 body: 3
2	ExprTuple	46
3	Conditional	value: 4 condition: 5
4	Operation	operator: 14 operand: 8
5	Operation	operator: 16 operands: 7
6	ExprTuple	8
7	ExprTuple	46, 9
8	Lambda	parameter: 45 body: 11
9	Literal
10	ExprTuple	45
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	45, 19
18	Lambda	parameters: 32 body: 20
19	Literal
20	Operation	operator: 21 operands: 22
21	Literal
22	ExprTuple	23, 24
23	Operation	operator: 26 operands: 25
24	Operation	operator: 26 operands: 27
25	ExprTuple	28, 29
26	Literal
27	ExprTuple	30, 31
28	Operation	operator: 34 operands: 32
29	Operation	operator: 36 operands: 33
30	Operation	operator: 34 operands: 35
31	Operation	operator: 36 operands: 37
32	ExprTuple	44, 40
33	ExprTuple	45, 40
34	Literal
35	ExprTuple	38, 40
36	Literal
37	ExprTuple	39, 40
38	Operation	operator: 42 operands: 41
39	Operation	operator: 42 operands: 43
40	Variable
41	ExprTuple	44, 46
42	Literal
43	ExprTuple	45, 46
44	Variable
45	Variable
46	Variable