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

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