Expression of type Lambda

from the theory of proveit.linear_algebra

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, S, T, V, W, v
from proveit.linear_algebra import LinMap, LinMapAdd
from proveit.logic import Equals, Forall
from proveit.numbers import Add

# build up the expression from sub-expressions
sub_expr1 = [v]
expr = Lambda([V, W], Forall(instance_param_or_params = [S, T], instance_expr = Forall(instance_param_or_params = sub_expr1, instance_expr = Equals(Function(LinMapAdd(S, T), sub_expr1), Add(Function(S, sub_expr1), Function(T, sub_expr1))), 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_{S, T \in \mathcal{L}\left(V, W\right)}~\left[\forall_{v \in V}~\left(\left(S + T\right)\left(v\right) = \left(S\left(v\right) + T\left(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	parameters: 25 body: 1
1	Operation	operator: 7 operand: 3
2	ExprTuple	3
3	Lambda	parameters: 34 body: 4
4	Conditional	value: 5 condition: 6
5	Operation	operator: 7 operand: 11
6	Operation	operator: 9 operands: 10
7	Literal
8	ExprTuple	11
9	Literal
10	ExprTuple	12, 13
11	Lambda	parameter: 40 body: 14
12	Operation	operator: 22 operands: 15
13	Operation	operator: 22 operands: 16
14	Conditional	value: 17 condition: 18
15	ExprTuple	37, 19
16	ExprTuple	38, 19
17	Operation	operator: 20 operands: 21
18	Operation	operator: 22 operands: 23
19	Operation	operator: 24 operands: 25
20	Literal
21	ExprTuple	26, 27
22	Literal
23	ExprTuple	40, 28
24	Literal
25	ExprTuple	28, 29
26	Operation	operator: 30 operand: 40
27	Operation	operator: 31 operands: 32
28	Variable
29	Variable
30	Operation	operator: 33 operands: 34
31	Literal
32	ExprTuple	35, 36
33	Literal
34	ExprTuple	37, 38
35	Operation	operator: 37 operand: 40
36	Operation	operator: 38 operand: 40
37	Variable
38	Variable
39	ExprTuple	40
40	Variable