Expression of type Conditional

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

# build up the expression from sub-expressions
expr = Conditional(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))), InSet(b, Complex))

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_{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) \textrm{ if } b \in \mathbb{C}\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: 3 operand: 7
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7
5	Literal
6	ExprTuple	33, 8
7	Lambda	parameters: 22 body: 9
8	Literal
9	Conditional	value: 10 condition: 11
10	Operation	operator: 13 operands: 12
11	Operation	operator: 13 operands: 14
12	ExprTuple	15, 16
13	Literal
14	ExprTuple	17, 18
15	Operation	operator: 21 operands: 19
16	Operation	operator: 21 operands: 20
17	Operation	operator: 21 operands: 22
18	Operation	operator: 23 operands: 24
19	ExprTuple	25, 27
20	ExprTuple	26, 27
21	Literal
22	ExprTuple	32, 27
23	Literal
24	ExprTuple	33, 27
25	Operation	operator: 28 operands: 29
26	Operation	operator: 30 operands: 31
27	Variable
28	Literal
29	ExprTuple	32, 34
30	Literal
31	ExprTuple	33, 34
32	Variable
33	Variable
34	Variable