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 Equals, Forall, InSet

# build up the expression from sub-expressions
sub_expr1 = [x]
expr = Lambda(K, Forall(instance_param_or_params = [V, W], instance_expr = 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)), domain = VecSpaces(K)))

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())

K \mapsto \left[\forall_{V, W \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)}~\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)\right]\right]

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 30 body: 1
1	Operation	operator: 7 operand: 3
2	ExprTuple	3
3	Lambda	parameters: 43 body: 4
4	Conditional	value: 5 condition: 6
5	Operation	operator: 7 operand: 10
6	Operation	operator: 22 operands: 9
7	Literal
8	ExprTuple	10
9	ExprTuple	11, 12
10	Lambda	parameters: 31 body: 13
11	Operation	operator: 15 operands: 14
12	Operation	operator: 15 operands: 16
13	Conditional	value: 17 condition: 18
14	ExprTuple	46, 19
15	Literal
16	ExprTuple	47, 19
17	Operation	operator: 20 operands: 21
18	Operation	operator: 22 operands: 23
19	Operation	operator: 24 operand: 30
20	Literal
21	ExprTuple	26, 27
22	Literal
23	ExprTuple	28, 29
24	Literal
25	ExprTuple	30
26	Operation	operator: 38 operands: 31
27	Lambda	parameter: 51 body: 32
28	Operation	operator: 40 operands: 33
29	Operation	operator: 40 operands: 34
30	Variable
31	ExprTuple	48, 49
32	Conditional	value: 35 condition: 36
33	ExprTuple	48, 37
34	ExprTuple	49, 37
35	Operation	operator: 38 operands: 39
36	Operation	operator: 40 operands: 41
37	Operation	operator: 42 operands: 43
38	Literal
39	ExprTuple	44, 45
40	Literal
41	ExprTuple	51, 46
42	Literal
43	ExprTuple	46, 47
44	Operation	operator: 48 operand: 51
45	Operation	operator: 49 operand: 51
46	Variable
47	Variable
48	Variable
49	Variable
50	ExprTuple	51
51	Variable