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 Conditional, ExprTuple, K, Lambda, V, a, x
from proveit.linear_algebra import ScalarMult, VecSpaces
from proveit.logic import Forall, InClass, InSet

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