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

# build up the expression from sub-expressions
sub_expr1 = [v]
expr = ExprTuple(Lambda([V, W], Forall(instance_param_or_params = [S, T], instance_expr = 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), domain = LinMap(V, W))))

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(V, W\right) \mapsto \left[\forall_{S, T \in \mathcal{L}\left(V, W\right)}~\left[\forall_{v \in V}~\left(\left(S + T\right)\left(v\right) = \left(S\left(v\right) + T\left(v\right)\right)\right)\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: 26 body: 2
2	Operation	operator: 8 operand: 4
3	ExprTuple	4
4	Lambda	parameters: 35 body: 5
5	Conditional	value: 6 condition: 7
6	Operation	operator: 8 operand: 12
7	Operation	operator: 10 operands: 11
8	Literal
9	ExprTuple	12
10	Literal
11	ExprTuple	13, 14
12	Lambda	parameter: 41 body: 15
13	Operation	operator: 23 operands: 16
14	Operation	operator: 23 operands: 17
15	Conditional	value: 18 condition: 19
16	ExprTuple	38, 20
17	ExprTuple	39, 20
18	Operation	operator: 21 operands: 22
19	Operation	operator: 23 operands: 24
20	Operation	operator: 25 operands: 26
21	Literal
22	ExprTuple	27, 28
23	Literal
24	ExprTuple	41, 29
25	Literal
26	ExprTuple	29, 30
27	Operation	operator: 31 operand: 41
28	Operation	operator: 32 operands: 33
29	Variable
30	Variable
31	Operation	operator: 34 operands: 35
32	Literal
33	ExprTuple	36, 37
34	Literal
35	ExprTuple	38, 39
36	Operation	operator: 38 operand: 41
37	Operation	operator: 39 operand: 41
38	Variable
39	Variable
40	ExprTuple	41
41	Variable