Expression of type Lambda

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

# build up the expression from sub-expressions
expr = Lambda(rho, Conditional(Forall(instance_param_or_params = [A, x], instance_expr = Equals(MatrixMult(MatrixExp(A, m), x), ScalarMult(Exp(e, Mult(two, pi, i, Mult(m, rho))), x)), condition = Equals(MatrixMult(A, x), ScalarMult(Exp(e, Mult(two, pi, i, rho)), x))), InSet(rho, Real)))

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())

\rho \mapsto \left\{\forall_{A, x~|~\left(A \thinspace x\right) = \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \rho} \cdot x\right)}~\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)\right) \textrm{ if } \rho \in \mathbb{R}\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 49 body: 2
1	ExprTuple	49
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	49, 10
9	Lambda	parameters: 24 body: 11
10	Literal
11	Conditional	value: 12 condition: 13
12	Operation	operator: 15 operands: 14
13	Operation	operator: 15 operands: 16
14	ExprTuple	17, 18
15	Literal
16	ExprTuple	19, 20
17	Operation	operator: 23 operands: 21
18	Operation	operator: 25 operands: 22
19	Operation	operator: 23 operands: 24
20	Operation	operator: 25 operands: 26
21	ExprTuple	27, 30
22	ExprTuple	28, 30
23	Literal
24	ExprTuple	36, 30
25	Literal
26	ExprTuple	29, 30
27	Operation	operator: 31 operands: 32
28	Operation	operator: 34 operands: 33
29	Operation	operator: 34 operands: 35
30	Variable
31	Literal
32	ExprTuple	36, 48
33	ExprTuple	38, 37
34	Literal
35	ExprTuple	38, 39
36	Variable
37	Operation	operator: 46 operands: 40
38	Literal
39	Operation	operator: 46 operands: 41
40	ExprTuple	43, 44, 45, 42
41	ExprTuple	43, 44, 45, 49
42	Operation	operator: 46 operands: 47
43	Literal
44	Literal
45	Literal
46	Literal
47	ExprTuple	48, 49
48	Variable
49	Variable