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

# build up the expression from sub-expressions
expr = Lambda([A, x], Conditional(Equals(MatrixMult(MatrixExp(A, m), x), MatrixMult(Exp(b, m), x)), Equals(MatrixMult(A, x), ScalarMult(b, 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(A, x\right) \mapsto \left\{\left(A^{m} \thinspace x\right) = \left(b^{m} \thinspace x\right) \textrm{ if } \left(A \thinspace x\right) = \left(b \cdot x\right)\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 14 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 5 operands: 4
3	Operation	operator: 5 operands: 6
4	ExprTuple	7, 8
5	Literal
6	ExprTuple	9, 10
7	Operation	operator: 13 operands: 11
8	Operation	operator: 13 operands: 12
9	Operation	operator: 13 operands: 14
10	Operation	operator: 15 operands: 16
11	ExprTuple	17, 19
12	ExprTuple	18, 19
13	Literal
14	ExprTuple	24, 19
15	Literal
16	ExprTuple	25, 19
17	Operation	operator: 20 operands: 21
18	Operation	operator: 22 operands: 23
19	Variable
20	Literal
21	ExprTuple	24, 26
22	Literal
23	ExprTuple	25, 26
24	Variable
25	Variable
26	Variable