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, Conditional, ExprTuple, Function, K, Lambda, V, W, x
from proveit.linear_algebra import LinMap, VecAdd, VecSpaces
from proveit.logic import And, Equals, Forall, InClass, InSet

# build up the expression from sub-expressions
sub_expr1 = [x]
sub_expr2 = VecSpaces(K)
expr = ExprTuple(Lambda([V, W], Conditional(Forall(instance_param_or_params = [A, B], instance_expr = Equals(VecAdd(A, B), Lambda(x, Conditional(VecAdd(Function(A, sub_expr1), Function(B, sub_expr1)), InSet(x, V)))), domain = LinMap(V, W)), And(InClass(V, sub_expr2), InClass(W, 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(V, W\right) \mapsto \left\{\forall_{A, B \in \mathcal{L}\left(V, W\right)}~\left(\left(A + B\right) = \left[x \mapsto \left\{A\left(x\right) + B\left(x\right) \textrm{ if } x \in V\right..\right]\right) \textrm{ if } V \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right) ,  W \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	parameters: 41 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 8
4	Operation	operator: 20 operands: 7
5	Literal
6	ExprTuple	8
7	ExprTuple	9, 10
8	Lambda	parameters: 29 body: 11
9	Operation	operator: 13 operands: 12
10	Operation	operator: 13 operands: 14
11	Conditional	value: 15 condition: 16
12	ExprTuple	44, 17
13	Literal
14	ExprTuple	45, 17
15	Operation	operator: 18 operands: 19
16	Operation	operator: 20 operands: 21
17	Operation	operator: 22 operand: 28
18	Literal
19	ExprTuple	24, 25
20	Literal
21	ExprTuple	26, 27
22	Literal
23	ExprTuple	28
24	Operation	operator: 36 operands: 29
25	Lambda	parameter: 49 body: 30
26	Operation	operator: 38 operands: 31
27	Operation	operator: 38 operands: 32
28	Variable
29	ExprTuple	46, 47
30	Conditional	value: 33 condition: 34
31	ExprTuple	46, 35
32	ExprTuple	47, 35
33	Operation	operator: 36 operands: 37
34	Operation	operator: 38 operands: 39
35	Operation	operator: 40 operands: 41
36	Literal
37	ExprTuple	42, 43
38	Literal
39	ExprTuple	49, 44
40	Literal
41	ExprTuple	44, 45
42	Operation	operator: 46 operand: 49
43	Operation	operator: 47 operand: 49
44	Variable
45	Variable
46	Variable
47	Variable
48	ExprTuple	49
49	Variable