Expression of type ExprTuple

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, ExprTuple, 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 = ExprTuple(Lambda(V, Conditional(Forall(instance_param_or_params = [x], instance_expr = Equals(VecAdd(x, sub_expr1), 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())

\left(V \mapsto \left\{\forall_{x \in V}~\left(\left(x + \vec{0}\left(V\right)\right) = \vec{0}\left(V\right)\right) \textrm{ if } V \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)\right..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameter: 29 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 9
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9
7	Literal
8	ExprTuple	29, 10
9	Lambda	parameter: 25 body: 12
10	Operation	operator: 13 operand: 17
11	ExprTuple	25
12	Conditional	value: 15 condition: 16
13	Literal
14	ExprTuple	17
15	Operation	operator: 18 operands: 19
16	Operation	operator: 20 operands: 21
17	Variable
18	Literal
19	ExprTuple	22, 26
20	Literal
21	ExprTuple	25, 29
22	Operation	operator: 23 operands: 24
23	Literal
24	ExprTuple	25, 26
25	Variable
26	Operation	operator: 27 operand: 29
27	Literal
28	ExprTuple	29
29	Variable