Expression of type Lambda

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, Lambda, 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 = Lambda([A, x], 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(A, x\right) \mapsto \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)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 13 body: 1
1	Operation	operator: 2 operands: 3
2	Literal
3	ExprTuple	4, 5
4	Operation	operator: 7 operands: 6
5	Operation	operator: 7 operands: 8
6	ExprTuple	9, 10
7	Literal
8	ExprTuple	11, 12
9	Operation	operator: 15 operands: 13
10	Operation	operator: 17 operands: 14
11	Operation	operator: 15 operands: 16
12	Operation	operator: 17 operands: 18
13	ExprTuple	25, 21
14	ExprTuple	26, 21
15	Literal
16	ExprTuple	19, 21
17	Literal
18	ExprTuple	20, 21
19	Operation	operator: 23 operands: 22
20	Operation	operator: 23 operands: 24
21	Variable
22	ExprTuple	25, 27
23	Literal
24	ExprTuple	26, 27
25	Variable
26	Variable
27	Variable