Expression of type Conditional

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, 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 = 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\{\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..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

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