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, m, rho, x
from proveit.linear_algebra import MatrixExp, MatrixMult, ScalarMult
from proveit.logic import Equals
from proveit.numbers import Exp, Mult, e, i, pi, two

# build up the expression from sub-expressions
expr = Conditional(Equals(MatrixMult(MatrixExp(A, m), x), ScalarMult(Exp(e, Mult(two, pi, i, Mult(m, rho))), x)), Equals(MatrixMult(A, x), ScalarMult(Exp(e, Mult(two, pi, i, rho)), x)))

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\{\left(A^{m} \thinspace x\right) = \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \left(m \cdot \rho\right)} \cdot x\right) \textrm{ if } \left(A \thinspace x\right) = \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \rho} \cdot x\right)\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: 4 operands: 3
2	Operation	operator: 4 operands: 5
3	ExprTuple	6, 7
4	Literal
5	ExprTuple	8, 9
6	Operation	operator: 12 operands: 10
7	Operation	operator: 14 operands: 11
8	Operation	operator: 12 operands: 13
9	Operation	operator: 14 operands: 15
10	ExprTuple	16, 19
11	ExprTuple	17, 19
12	Literal
13	ExprTuple	25, 19
14	Literal
15	ExprTuple	18, 19
16	Operation	operator: 20 operands: 21
17	Operation	operator: 23 operands: 22
18	Operation	operator: 23 operands: 24
19	Variable
20	Literal
21	ExprTuple	25, 37
22	ExprTuple	27, 26
23	Literal
24	ExprTuple	27, 28
25	Variable
26	Operation	operator: 35 operands: 29
27	Literal
28	Operation	operator: 35 operands: 30
29	ExprTuple	32, 33, 34, 31
30	ExprTuple	32, 33, 34, 38
31	Operation	operator: 35 operands: 36
32	Literal
33	Literal
34	Literal
35	Literal
36	ExprTuple	37, 38
37	Variable
38	Variable