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, 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 = 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(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..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 40 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 4 operand: 7
3	Operation	operator: 19 operands: 6
4	Literal
5	ExprTuple	7
6	ExprTuple	8, 9
7	Lambda	parameters: 28 body: 10
8	Operation	operator: 12 operands: 11
9	Operation	operator: 12 operands: 13
10	Conditional	value: 14 condition: 15
11	ExprTuple	43, 16
12	Literal
13	ExprTuple	44, 16
14	Operation	operator: 17 operands: 18
15	Operation	operator: 19 operands: 20
16	Operation	operator: 21 operand: 27
17	Literal
18	ExprTuple	23, 24
19	Literal
20	ExprTuple	25, 26
21	Literal
22	ExprTuple	27
23	Operation	operator: 35 operands: 28
24	Lambda	parameter: 48 body: 29
25	Operation	operator: 37 operands: 30
26	Operation	operator: 37 operands: 31
27	Variable
28	ExprTuple	45, 46
29	Conditional	value: 32 condition: 33
30	ExprTuple	45, 34
31	ExprTuple	46, 34
32	Operation	operator: 35 operands: 36
33	Operation	operator: 37 operands: 38
34	Operation	operator: 39 operands: 40
35	Literal
36	ExprTuple	41, 42
37	Literal
38	ExprTuple	48, 43
39	Literal
40	ExprTuple	43, 44
41	Operation	operator: 45 operand: 48
42	Operation	operator: 46 operand: 48
43	Variable
44	Variable
45	Variable
46	Variable
47	ExprTuple	48
48	Variable