Expression of type Lambda

from the theory of proveit.linear_algebra.scalar_multiplication

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 Conditional, K, Lambda, alpha, beta, x
from proveit.linear_algebra import ScalarMult
from proveit.logic import And, Equals, InSet

# build up the expression from sub-expressions
expr = Lambda([alpha, beta], Conditional(Equals(ScalarMult(alpha, ScalarMult(beta, x)), ScalarMult(ScalarMult(alpha, beta), x)), And(InSet(alpha, K), InSet(beta, K))))

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(\alpha, \beta\right) \mapsto \left\{\left(\alpha \cdot \left(\beta \cdot x\right)\right) = \left(\left(\alpha \cdot \beta\right) \cdot x\right) \textrm{ if } \alpha \in K ,  \beta \in K\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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