Expression of type Implies

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, b, k, x
from proveit.linear_algebra import MatrixMult, ScalarMult
from proveit.logic import Equals, Implies
from proveit.numbers import Exp

# build up the expression from sub-expressions
expr = Implies(Equals(MatrixMult(A, x), ScalarMult(b, x)), Equals(MatrixMult(Exp(A, k), x), ScalarMult(Exp(b, k), 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 \thinspace x\right) = \left(b \cdot x\right)\right) \Rightarrow \left(\left(A^{k} \thinspace x\right) = \left(b^{k} \cdot x\right)\right)

stored_expr.style_options()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix
wrap_positions	position(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.	()	()	('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)
direction	Direction of the relation (normal or reversed)	normal	normal	('with_direction_reversed', 'is_reversed')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operands: 2
1	Literal
2	ExprTuple	3, 4
3	Operation	operator: 6 operands: 5
4	Operation	operator: 6 operands: 7
5	ExprTuple	8, 9
6	Literal
7	ExprTuple	10, 11
8	Operation	operator: 14 operands: 12
9	Operation	operator: 16 operands: 13
10	Operation	operator: 14 operands: 15
11	Operation	operator: 16 operands: 17
12	ExprTuple	24, 20
13	ExprTuple	25, 20
14	Literal
15	ExprTuple	18, 20
16	Literal
17	ExprTuple	19, 20
18	Operation	operator: 22 operands: 21
19	Operation	operator: 22 operands: 23
20	Variable
21	ExprTuple	24, 26
22	Literal
23	ExprTuple	25, 26
24	Variable
25	Variable
26	Variable