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 Conditional, Function, Lambda, P, Px, V, W, x, y
from proveit.linear_algebra import LinMap, VecAdd
from proveit.logic import Equals, Forall, InSet

# build up the expression from sub-expressions
expr = Lambda(P, Conditional(Forall(instance_param_or_params = [x, y], instance_expr = Equals(Function(P, [VecAdd(x, y)]), VecAdd(Px, Function(P, [y]))), domain = V), InSet(P, LinMap(V, W))))

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())

P \mapsto \left\{\forall_{x, y \in V}~\left(P\left(x + y\right) = \left(P\left(x\right) + P\left(y\right)\right)\right) \textrm{ if } P \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	parameter: 36 body: 2
1	ExprTuple	36
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 8
4	Operation	operator: 27 operands: 7
5	Literal
6	ExprTuple	8
7	ExprTuple	36, 9
8	Lambda	parameters: 34 body: 10
9	Operation	operator: 11 operands: 12
10	Conditional	value: 13 condition: 14
11	Literal
12	ExprTuple	32, 15
13	Operation	operator: 16 operands: 17
14	Operation	operator: 18 operands: 19
15	Variable
16	Literal
17	ExprTuple	20, 21
18	Literal
19	ExprTuple	22, 23
20	Operation	operator: 36 operand: 29
21	Operation	operator: 33 operands: 25
22	Operation	operator: 27 operands: 26
23	Operation	operator: 27 operands: 28
24	ExprTuple	29
25	ExprTuple	30, 31
26	ExprTuple	38, 32
27	Literal
28	ExprTuple	39, 32
29	Operation	operator: 33 operands: 34
30	Operation	operator: 36 operand: 38
31	Operation	operator: 36 operand: 39
32	Variable
33	Literal
34	ExprTuple	38, 39
35	ExprTuple	38
36	Variable
37	ExprTuple	39
38	Variable
39	Variable