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 ExprTuple, 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 = ExprTuple(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())

\left(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]\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: 20 body: 2
2	Operation	operator: 8 operand: 4
3	ExprTuple	4
4	Lambda	parameter: 32 body: 5
5	Conditional	value: 6 condition: 7
6	Operation	operator: 8 operand: 12
7	Operation	operator: 10 operands: 11
8	Literal
9	ExprTuple	12
10	Literal
11	ExprTuple	32, 13
12	Lambda	parameter: 28 body: 15
13	Operation	operator: 16 operand: 20
14	ExprTuple	28
15	Conditional	value: 18 condition: 19
16	Literal
17	ExprTuple	20
18	Operation	operator: 21 operands: 22
19	Operation	operator: 23 operands: 24
20	Variable
21	Literal
22	ExprTuple	25, 29
23	Literal
24	ExprTuple	28, 32
25	Operation	operator: 26 operands: 27
26	Literal
27	ExprTuple	28, 29
28	Variable
29	Operation	operator: 30 operand: 32
30	Literal
31	ExprTuple	32
32	Variable