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, Lambda, V, W, x
from proveit.linear_algebra import LinMap, VecAdd
from proveit.logic import And, Equals, InSet

# build up the expression from sub-expressions
sub_expr1 = [x]
sub_expr2 = LinMap(V, W)
expr = ExprTuple(Lambda([A, B], Conditional(Equals(VecAdd(A, B), Lambda(x, Conditional(VecAdd(Function(A, sub_expr1), Function(B, sub_expr1)), InSet(x, V)))), And(InSet(A, sub_expr2), InSet(B, 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(A, B\right) \mapsto \left\{\left(A + B\right) = \left[x \mapsto \left\{A\left(x\right) + B\left(x\right) \textrm{ if } x \in V\right..\right] \textrm{ if } A \in \mathcal{L}\left(V, W\right) ,  B \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: 13 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9, 10
7	Literal
8	ExprTuple	11, 12
9	Operation	operator: 20 operands: 13
10	Lambda	parameter: 33 body: 14
11	Operation	operator: 22 operands: 15
12	Operation	operator: 22 operands: 16
13	ExprTuple	30, 31
14	Conditional	value: 17 condition: 18
15	ExprTuple	30, 19
16	ExprTuple	31, 19
17	Operation	operator: 20 operands: 21
18	Operation	operator: 22 operands: 23
19	Operation	operator: 24 operands: 25
20	Literal
21	ExprTuple	26, 27
22	Literal
23	ExprTuple	33, 28
24	Literal
25	ExprTuple	28, 29
26	Operation	operator: 30 operand: 33
27	Operation	operator: 31 operand: 33
28	Variable
29	Variable
30	Variable
31	Variable
32	ExprTuple	33
33	Variable