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 ExprTuple, Function, Lambda, P, Px, V, W, x, y
from proveit.linear_algebra import LinMap, VecAdd
from proveit.logic import Equals, Forall

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([V, W], Forall(instance_param_or_params = [P], instance_expr = Forall(instance_param_or_params = [x, y], instance_expr = Equals(Function(P, [VecAdd(x, y)]), VecAdd(Px, Function(P, [y]))), 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_{P \in \mathcal{L}\left(V, W\right)}~\left[\forall_{x, y \in V}~\left(P\left(x + y\right) = \left(P\left(x\right) + P\left(y\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: 16 body: 2
2	Operation	operator: 9 operand: 4
3	ExprTuple	4
4	Lambda	parameter: 40 body: 6
5	ExprTuple	40
6	Conditional	value: 7 condition: 8
7	Operation	operator: 9 operand: 12
8	Operation	operator: 31 operands: 11
9	Literal
10	ExprTuple	12
11	ExprTuple	40, 13
12	Lambda	parameters: 38 body: 14
13	Operation	operator: 15 operands: 16
14	Conditional	value: 17 condition: 18
15	Literal
16	ExprTuple	36, 19
17	Operation	operator: 20 operands: 21
18	Operation	operator: 22 operands: 23
19	Variable
20	Literal
21	ExprTuple	24, 25
22	Literal
23	ExprTuple	26, 27
24	Operation	operator: 40 operand: 33
25	Operation	operator: 37 operands: 29
26	Operation	operator: 31 operands: 30
27	Operation	operator: 31 operands: 32
28	ExprTuple	33
29	ExprTuple	34, 35
30	ExprTuple	42, 36
31	Literal
32	ExprTuple	43, 36
33	Operation	operator: 37 operands: 38
34	Operation	operator: 40 operand: 42
35	Operation	operator: 40 operand: 43
36	Variable
37	Literal
38	ExprTuple	42, 43
39	ExprTuple	42
40	Variable
41	ExprTuple	43
42	Variable
43	Variable