Expression of type ExprTuple

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, ExprTuple, Lambda, b, k, x
from proveit.linear_algebra import MatrixMult, ScalarMult
from proveit.logic import Equals, Implies
from proveit.numbers import Exp

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([A, x], Implies(Equals(MatrixMult(A, x), ScalarMult(b, x)), Equals(MatrixMult(Exp(A, k), x), ScalarMult(Exp(b, k), 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(\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)\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: 14 body: 2
2	Operation	operator: 3 operands: 4
3	Literal
4	ExprTuple	5, 6
5	Operation	operator: 8 operands: 7
6	Operation	operator: 8 operands: 9
7	ExprTuple	10, 11
8	Literal
9	ExprTuple	12, 13
10	Operation	operator: 16 operands: 14
11	Operation	operator: 18 operands: 15
12	Operation	operator: 16 operands: 17
13	Operation	operator: 18 operands: 19
14	ExprTuple	26, 22
15	ExprTuple	27, 22
16	Literal
17	ExprTuple	20, 22
18	Literal
19	ExprTuple	21, 22
20	Operation	operator: 24 operands: 23
21	Operation	operator: 24 operands: 25
22	Variable
23	ExprTuple	26, 28
24	Literal
25	ExprTuple	27, 28
26	Variable
27	Variable
28	Variable