Expression of type Lambda

from the theory of proveit.linear_algebra.linear_maps

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, B, Composition, Conditional, Lambda, V
from proveit.linear_algebra import AntiCommutator, VecAdd
from proveit.logic import And, Equals, InSet

# build up the expression from sub-expressions
expr = Lambda([A, B], Conditional(Equals(AntiCommutator(A, B), VecAdd(Composition(A, B), Composition(B, A))), And(InSet(A, V), InSet(B, V))))

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, B\right) \mapsto \left\{\left\{A, B\right\} = \left(\left(A \circ B\right) + \left(B \circ A\right)\right) \textrm{ if } A \in V ,  B \in V\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 21 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: 12 operands: 21
9	Operation	operator: 13 operands: 14
10	Operation	operator: 16 operands: 15
11	Operation	operator: 16 operands: 17
12	Literal
13	Literal
14	ExprTuple	18, 19
15	ExprTuple	25, 20
16	Literal
17	ExprTuple	24, 20
18	Operation	operator: 22 operands: 21
19	Operation	operator: 22 operands: 23
20	Variable
21	ExprTuple	25, 24
22	Literal
23	ExprTuple	24, 25
24	Variable
25	Variable