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
from proveit.numbers import Exp

# build up the expression from sub-expressions
expr = Conditional(Equals(MatrixMult(MatrixExp(A, m), x), MatrixMult(Exp(b, m), x)), Equals(MatrixMult(A, x), ScalarMult(b, 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(b^{m} \thinspace x\right) \textrm{ if } \left(A \thinspace x\right) = \left(b \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: 12 operands: 11
8	Operation	operator: 12 operands: 13
9	Operation	operator: 14 operands: 15
10	ExprTuple	16, 18
11	ExprTuple	17, 18
12	Literal
13	ExprTuple	23, 18
14	Literal
15	ExprTuple	24, 18
16	Operation	operator: 19 operands: 20
17	Operation	operator: 21 operands: 22
18	Variable
19	Literal
20	ExprTuple	23, 25
21	Literal
22	ExprTuple	24, 25
23	Variable
24	Variable
25	Variable