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

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

\left(V, W\right) \mapsto \left[\forall_{P \in \mathcal{L}\left(V, W\right)}~\left[\forall_{x, y \in V}~\left(P\left(x + y\right) = \left(P\left(x\right) + P\left(y\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	parameters: 15 body: 1
1	Operation	operator: 8 operand: 3
2	ExprTuple	3
3	Lambda	parameter: 39 body: 5
4	ExprTuple	39
5	Conditional	value: 6 condition: 7
6	Operation	operator: 8 operand: 11
7	Operation	operator: 30 operands: 10
8	Literal
9	ExprTuple	11
10	ExprTuple	39, 12
11	Lambda	parameters: 37 body: 13
12	Operation	operator: 14 operands: 15
13	Conditional	value: 16 condition: 17
14	Literal
15	ExprTuple	35, 18
16	Operation	operator: 19 operands: 20
17	Operation	operator: 21 operands: 22
18	Variable
19	Literal
20	ExprTuple	23, 24
21	Literal
22	ExprTuple	25, 26
23	Operation	operator: 39 operand: 32
24	Operation	operator: 36 operands: 28
25	Operation	operator: 30 operands: 29
26	Operation	operator: 30 operands: 31
27	ExprTuple	32
28	ExprTuple	33, 34
29	ExprTuple	41, 35
30	Literal
31	ExprTuple	42, 35
32	Operation	operator: 36 operands: 37
33	Operation	operator: 39 operand: 41
34	Operation	operator: 39 operand: 42
35	Variable
36	Literal
37	ExprTuple	41, 42
38	ExprTuple	41
39	Variable
40	ExprTuple	42
41	Variable
42	Variable