Expression of type Lambda

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, 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 = 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(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..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 12 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 4 operands: 5
3	Operation	operator: 6 operands: 7
4	Literal
5	ExprTuple	8, 9
6	Literal
7	ExprTuple	10, 11
8	Operation	operator: 19 operands: 12
9	Lambda	parameter: 32 body: 13
10	Operation	operator: 21 operands: 14
11	Operation	operator: 21 operands: 15
12	ExprTuple	29, 30
13	Conditional	value: 16 condition: 17
14	ExprTuple	29, 18
15	ExprTuple	30, 18
16	Operation	operator: 19 operands: 20
17	Operation	operator: 21 operands: 22
18	Operation	operator: 23 operands: 24
19	Literal
20	ExprTuple	25, 26
21	Literal
22	ExprTuple	32, 27
23	Literal
24	ExprTuple	27, 28
25	Operation	operator: 29 operand: 32
26	Operation	operator: 30 operand: 32
27	Variable
28	Variable
29	Variable
30	Variable
31	ExprTuple	32
32	Variable