Expression of type ExprTuple

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, ExprTuple, Lambda, V
from proveit.linear_algebra import Commutator, VecAdd, VecNeg
from proveit.logic import And, Equals, InSet

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([A, B], Conditional(Equals(Commutator(A, B), VecAdd(Composition(A, B), VecNeg(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(\left(A, B\right) \mapsto \left\{\left[A, B\right] = \left(\left(A \circ B\right) + \left(-\left(B \circ A\right)\right)\right) \textrm{ if } A \in V ,  B \in V\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: 22 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9, 10
7	Literal
8	ExprTuple	11, 12
9	Operation	operator: 13 operands: 22
10	Operation	operator: 14 operands: 15
11	Operation	operator: 17 operands: 16
12	Operation	operator: 17 operands: 18
13	Literal
14	Literal
15	ExprTuple	19, 20
16	ExprTuple	29, 21
17	Literal
18	ExprTuple	28, 21
19	Operation	operator: 26 operands: 22
20	Operation	operator: 23 operand: 25
21	Variable
22	ExprTuple	29, 28
23	Literal
24	ExprTuple	25
25	Operation	operator: 26 operands: 27
26	Literal
27	ExprTuple	28, 29
28	Variable
29	Variable