Expression of type ExprTuple

from the theory of proveit.linear_algebra.scalar_multiplication

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, a, x
from proveit.linear_algebra import ScalarMult, VecSpaces
from proveit.logic import Forall, InSet

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(K, Forall(instance_param_or_params = [V], instance_expr = Forall(instance_param_or_params = [a], instance_expr = Forall(instance_param_or_params = [x], instance_expr = InSet(ScalarMult(a, x), V), domain = V), domain = K), 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_{a \in K}~\left[\forall_{x \in V}~\left(\left(a \cdot x\right) \in 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: 24 body: 2
2	Operation	operator: 20 operand: 4
3	ExprTuple	4
4	Lambda	parameter: 33 body: 6
5	ExprTuple	33
6	Conditional	value: 7 condition: 8
7	Operation	operator: 20 operand: 12
8	Operation	operator: 10 operands: 11
9	ExprTuple	12
10	Literal
11	ExprTuple	33, 13
12	Lambda	parameter: 36 body: 15
13	Operation	operator: 16 operand: 24
14	ExprTuple	36
15	Conditional	value: 18 condition: 19
16	Literal
17	ExprTuple	24
18	Operation	operator: 20 operand: 23
19	Operation	operator: 30 operands: 22
20	Literal
21	ExprTuple	23
22	ExprTuple	36, 24
23	Lambda	parameter: 37 body: 26
24	Variable
25	ExprTuple	37
26	Conditional	value: 27 condition: 28
27	Operation	operator: 30 operands: 29
28	Operation	operator: 30 operands: 31
29	ExprTuple	32, 33
30	Literal
31	ExprTuple	37, 33
32	Operation	operator: 34 operands: 35
33	Variable
34	Literal
35	ExprTuple	36, 37
36	Variable
37	Variable