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

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

K \mapsto \left[\forall_{V \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)}~\left[\forall_{x \in V}~\left(\left(x + \vec{0}\left(V\right)\right) = \vec{0}\left(V\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	parameter: 19 body: 1
1	Operation	operator: 7 operand: 3
2	ExprTuple	3
3	Lambda	parameter: 31 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	31, 12
11	Lambda	parameter: 27 body: 14
12	Operation	operator: 15 operand: 19
13	ExprTuple	27
14	Conditional	value: 17 condition: 18
15	Literal
16	ExprTuple	19
17	Operation	operator: 20 operands: 21
18	Operation	operator: 22 operands: 23
19	Variable
20	Literal
21	ExprTuple	24, 28
22	Literal
23	ExprTuple	27, 31
24	Operation	operator: 25 operands: 26
25	Literal
26	ExprTuple	27, 28
27	Variable
28	Operation	operator: 29 operand: 31
29	Literal
30	ExprTuple	31
31	Variable