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, b, m, x
from proveit.linear_algebra import MatrixExp, MatrixMult, ScalarMult
from proveit.logic import Equals, Forall, InSet
from proveit.numbers import Complex, Exp

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

\left(b \mapsto \left\{\forall_{A, x~|~\left(A \thinspace x\right) = \left(b \cdot x\right)}~\left(\left(A^{m} \thinspace x\right) = \left(b^{m} \thinspace x\right)\right) \textrm{ if } b \in \mathbb{C}\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: 36 body: 3
2	ExprTuple	36
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 10
5	Operation	operator: 8 operands: 9
6	Literal
7	ExprTuple	10
8	Literal
9	ExprTuple	36, 11
10	Lambda	parameters: 25 body: 12
11	Literal
12	Conditional	value: 13 condition: 14
13	Operation	operator: 16 operands: 15
14	Operation	operator: 16 operands: 17
15	ExprTuple	18, 19
16	Literal
17	ExprTuple	20, 21
18	Operation	operator: 24 operands: 22
19	Operation	operator: 24 operands: 23
20	Operation	operator: 24 operands: 25
21	Operation	operator: 26 operands: 27
22	ExprTuple	28, 30
23	ExprTuple	29, 30
24	Literal
25	ExprTuple	35, 30
26	Literal
27	ExprTuple	36, 30
28	Operation	operator: 31 operands: 32
29	Operation	operator: 33 operands: 34
30	Variable
31	Literal
32	ExprTuple	35, 37
33	Literal
34	ExprTuple	36, 37
35	Variable
36	Variable
37	Variable