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
from proveit.numbers import Exp, Mult, e, i, pi, two

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([A, x], Conditional(Equals(MatrixMult(MatrixExp(A, m), x), ScalarMult(Exp(e, Mult(two, pi, i, Mult(m, rho))), x)), Equals(MatrixMult(A, x), ScalarMult(Exp(e, Mult(two, pi, i, rho)), 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, x\right) \mapsto \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) \textrm{ if } \left(A \thinspace x\right) = \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \rho} \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	ExprTuple	1
1	Lambda	parameters: 15 body: 2
2	Conditional	value: 3 condition: 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	18, 21
13	ExprTuple	19, 21
14	Literal
15	ExprTuple	27, 21
16	Literal
17	ExprTuple	20, 21
18	Operation	operator: 22 operands: 23
19	Operation	operator: 25 operands: 24
20	Operation	operator: 25 operands: 26
21	Variable
22	Literal
23	ExprTuple	27, 39
24	ExprTuple	29, 28
25	Literal
26	ExprTuple	29, 30
27	Variable
28	Operation	operator: 37 operands: 31
29	Literal
30	Operation	operator: 37 operands: 32
31	ExprTuple	34, 35, 36, 33
32	ExprTuple	34, 35, 36, 40
33	Operation	operator: 37 operands: 38
34	Literal
35	Literal
36	Literal
37	Literal
38	ExprTuple	39, 40
39	Variable
40	Variable