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, Conditional, Lambda, b, k, x
from proveit.linear_algebra import MatrixMult, ScalarMult
from proveit.logic import Equals, Forall, Implies, InSet
from proveit.numbers import Complex, Exp

# build up the expression from sub-expressions
expr = Lambda(b, Conditional(Forall(instance_param_or_params = [A, x], instance_expr = Implies(Equals(MatrixMult(A, x), ScalarMult(b, x)), Equals(MatrixMult(Exp(A, k), x), ScalarMult(Exp(b, k), 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())

b \mapsto \left\{\forall_{A, x}~\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) \textrm{ if } b \in \mathbb{C}\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 36 body: 2
1	ExprTuple	36
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 9
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9
7	Literal
8	ExprTuple	36, 10
9	Lambda	parameters: 23 body: 11
10	Literal
11	Operation	operator: 12 operands: 13
12	Literal
13	ExprTuple	14, 15
14	Operation	operator: 17 operands: 16
15	Operation	operator: 17 operands: 18
16	ExprTuple	19, 20
17	Literal
18	ExprTuple	21, 22
19	Operation	operator: 25 operands: 23
20	Operation	operator: 27 operands: 24
21	Operation	operator: 25 operands: 26
22	Operation	operator: 27 operands: 28
23	ExprTuple	35, 31
24	ExprTuple	36, 31
25	Literal
26	ExprTuple	29, 31
27	Literal
28	ExprTuple	30, 31
29	Operation	operator: 33 operands: 32
30	Operation	operator: 33 operands: 34
31	Variable
32	ExprTuple	35, 37
33	Literal
34	ExprTuple	36, 37
35	Variable
36	Variable
37	Variable