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, K, Lambda, V
from proveit.linear_algebra import Commutator, VecAdd, VecNeg, VecSpaces
from proveit.logic import Equals, Forall, InClass

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(V, Conditional(Forall(instance_param_or_params = [A, B], instance_expr = Equals(Commutator(A, B), VecAdd(Composition(A, B), VecNeg(Composition(B, A)))), domain = V), InClass(V, VecSpaces(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(V \mapsto \left\{\forall_{A, B \in V}~\left(\left[A, B\right] = \left(\left(A \circ B\right) + \left(-\left(B \circ A\right)\right)\right)\right) \textrm{ if } V \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\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	parameter: 34 body: 3
2	ExprTuple	34
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 10
5	Operation	operator: 8 operands: 9
6	Literal
7	ExprTuple	10
8	Literal
9	ExprTuple	34, 11
10	Lambda	parameters: 35 body: 12
11	Operation	operator: 13 operand: 17
12	Conditional	value: 15 condition: 16
13	Literal
14	ExprTuple	17
15	Operation	operator: 18 operands: 19
16	Operation	operator: 20 operands: 21
17	Variable
18	Literal
19	ExprTuple	22, 23
20	Literal
21	ExprTuple	24, 25
22	Operation	operator: 26 operands: 35
23	Operation	operator: 27 operands: 28
24	Operation	operator: 30 operands: 29
25	Operation	operator: 30 operands: 31
26	Literal
27	Literal
28	ExprTuple	32, 33
29	ExprTuple	42, 34
30	Literal
31	ExprTuple	41, 34
32	Operation	operator: 39 operands: 35
33	Operation	operator: 36 operand: 38
34	Variable
35	ExprTuple	42, 41
36	Literal
37	ExprTuple	38
38	Operation	operator: 39 operands: 40
39	Literal
40	ExprTuple	41, 42
41	Variable
42	Variable