Expression of type ExprTuple

from the theory of proveit.linear_algebra

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, ExprTuple, Function, Lambda, S, T, V, W, v
from proveit.linear_algebra import LinMap, LinMapAdd
from proveit.logic import And, Equals, Forall, InSet
from proveit.numbers import Add

# build up the expression from sub-expressions
sub_expr1 = [v]
sub_expr2 = LinMap(V, W)
expr = ExprTuple(Lambda([S, T], Conditional(Forall(instance_param_or_params = sub_expr1, instance_expr = Equals(Function(LinMapAdd(S, T), sub_expr1), Add(Function(S, sub_expr1), Function(T, sub_expr1))), domain = V), And(InSet(S, sub_expr2), InSet(T, sub_expr2)))))

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(S, T\right) \mapsto \left\{\forall_{v \in V}~\left(\left(S + T\right)\left(v\right) = \left(S\left(v\right) + T\left(v\right)\right)\right) \textrm{ if } S \in \mathcal{L}\left(V, W\right) ,  T \in \mathcal{L}\left(V, W\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	parameters: 32 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 9
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9
7	Literal
8	ExprTuple	10, 11
9	Lambda	parameter: 38 body: 12
10	Operation	operator: 20 operands: 13
11	Operation	operator: 20 operands: 14
12	Conditional	value: 15 condition: 16
13	ExprTuple	35, 17
14	ExprTuple	36, 17
15	Operation	operator: 18 operands: 19
16	Operation	operator: 20 operands: 21
17	Operation	operator: 22 operands: 23
18	Literal
19	ExprTuple	24, 25
20	Literal
21	ExprTuple	38, 26
22	Literal
23	ExprTuple	26, 27
24	Operation	operator: 28 operand: 38
25	Operation	operator: 29 operands: 30
26	Variable
27	Variable
28	Operation	operator: 31 operands: 32
29	Literal
30	ExprTuple	33, 34
31	Literal
32	ExprTuple	35, 36
33	Operation	operator: 35 operand: 38
34	Operation	operator: 36 operand: 38
35	Variable
36	Variable
37	ExprTuple	38
38	Variable