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 Conditional, Function, Lambda, S, T, V, W, v
from proveit.linear_algebra import LinMap, LinMapAdd
from proveit.logic import And, Equals, Forall, InSet
from proveit.numbers import Add

# build up the expression from sub-expressions
sub_expr1 = [v]
sub_expr2 = LinMap(V, W)
expr = Lambda([S, T], Conditional(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), And(InSet(S, sub_expr2), InSet(T, 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(S, T\right) \mapsto \left\{\forall_{v \in V}~\left(\left(S + T\right)\left(v\right) = \left(S\left(v\right) + T\left(v\right)\right)\right) \textrm{ if } S \in \mathcal{L}\left(V, W\right) ,  T \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	parameters: 31 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 4 operand: 8
3	Operation	operator: 6 operands: 7
4	Literal
5	ExprTuple	8
6	Literal
7	ExprTuple	9, 10
8	Lambda	parameter: 37 body: 11
9	Operation	operator: 19 operands: 12
10	Operation	operator: 19 operands: 13
11	Conditional	value: 14 condition: 15
12	ExprTuple	34, 16
13	ExprTuple	35, 16
14	Operation	operator: 17 operands: 18
15	Operation	operator: 19 operands: 20
16	Operation	operator: 21 operands: 22
17	Literal
18	ExprTuple	23, 24
19	Literal
20	ExprTuple	37, 25
21	Literal
22	ExprTuple	25, 26
23	Operation	operator: 27 operand: 37
24	Operation	operator: 28 operands: 29
25	Variable
26	Variable
27	Operation	operator: 30 operands: 31
28	Literal
29	ExprTuple	32, 33
30	Literal
31	ExprTuple	34, 35
32	Operation	operator: 34 operand: 37
33	Operation	operator: 35 operand: 37
34	Variable
35	Variable
36	ExprTuple	37
37	Variable