Expression of type ExprTuple

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, ExprTuple, 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, NaturalPos, Real, e, i, pi, two

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(m, Conditional(Forall(instance_param_or_params = [rho], instance_expr = 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))), domain = Real), InSet(m, NaturalPos))))

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(m \mapsto \left\{\forall_{\rho \in \mathbb{R}}~\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)\right] \textrm{ if } m \in \mathbb{N}^+\right..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameter: 57 body: 3
2	ExprTuple	57
3	Conditional	value: 4 condition: 5
4	Operation	operator: 14 operand: 8
5	Operation	operator: 16 operands: 7
6	ExprTuple	8
7	ExprTuple	57, 9
8	Lambda	parameter: 58 body: 11
9	Literal
10	ExprTuple	58
11	Conditional	value: 12 condition: 13
12	Operation	operator: 14 operand: 18
13	Operation	operator: 16 operands: 17
14	Literal
15	ExprTuple	18
16	Literal
17	ExprTuple	58, 19
18	Lambda	parameters: 33 body: 20
19	Literal
20	Conditional	value: 21 condition: 22
21	Operation	operator: 24 operands: 23
22	Operation	operator: 24 operands: 25
23	ExprTuple	26, 27
24	Literal
25	ExprTuple	28, 29
26	Operation	operator: 32 operands: 30
27	Operation	operator: 34 operands: 31
28	Operation	operator: 32 operands: 33
29	Operation	operator: 34 operands: 35
30	ExprTuple	36, 39
31	ExprTuple	37, 39
32	Literal
33	ExprTuple	45, 39
34	Literal
35	ExprTuple	38, 39
36	Operation	operator: 40 operands: 41
37	Operation	operator: 43 operands: 42
38	Operation	operator: 43 operands: 44
39	Variable
40	Literal
41	ExprTuple	45, 57
42	ExprTuple	47, 46
43	Literal
44	ExprTuple	47, 48
45	Variable
46	Operation	operator: 55 operands: 49
47	Literal
48	Operation	operator: 55 operands: 50
49	ExprTuple	52, 53, 54, 51
50	ExprTuple	52, 53, 54, 58
51	Operation	operator: 55 operands: 56
52	Literal
53	Literal
54	Literal
55	Literal
56	ExprTuple	57, 58
57	Variable
58	Variable