Expression of type Lambda

from the theory of proveit.linear_algebra.addition

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, K, Lambda, V, x
from proveit.linear_algebra import VecAdd, VecSpaces, VecZero
from proveit.logic import Equals, Forall, InClass

# build up the expression from sub-expressions
sub_expr1 = VecZero(V)
expr = Lambda(V, Conditional(Forall(instance_param_or_params = [x], instance_expr = Equals(VecAdd(sub_expr1, x), sub_expr1), domain = V), InClass(V, 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())

V \mapsto \left\{\forall_{x \in V}~\left(\left(\vec{0}\left(V\right) + x\right) = \vec{0}\left(V\right)\right) \textrm{ if } V \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\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: 28 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	28, 9
8	Lambda	parameter: 25 body: 11
9	Operation	operator: 12 operand: 16
10	ExprTuple	25
11	Conditional	value: 14 condition: 15
12	Literal
13	ExprTuple	16
14	Operation	operator: 17 operands: 18
15	Operation	operator: 19 operands: 20
16	Variable
17	Literal
18	ExprTuple	21, 24
19	Literal
20	ExprTuple	25, 28
21	Operation	operator: 22 operands: 23
22	Literal
23	ExprTuple	24, 25
24	Operation	operator: 26 operand: 28
25	Variable
26	Literal
27	ExprTuple	28
28	Variable