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, b, x, y
from proveit.linear_algebra import binary_lin_comb_ax_by
from proveit.logic import And, Forall, InSet

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([a, b], Conditional(Forall(instance_param_or_params = [x, y], instance_expr = InSet(binary_lin_comb_ax_by, V), domain = V), And(InSet(a, K), InSet(b, 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(\left(a, b\right) \mapsto \left\{\forall_{x, y \in V}~\left(\left(\left(a \cdot x\right) + \left(b \cdot y\right)\right) \in V\right) \textrm{ if } a \in K ,  b \in K\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	parameters: 2 body: 3
2	ExprTuple	36, 38
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 9
5	Operation	operator: 20 operands: 8
6	Literal
7	ExprTuple	9
8	ExprTuple	10, 11
9	Lambda	parameters: 12 body: 13
10	Operation	operator: 28 operands: 14
11	Operation	operator: 28 operands: 15
12	ExprTuple	37, 39
13	Conditional	value: 16 condition: 17
14	ExprTuple	36, 18
15	ExprTuple	38, 18
16	Operation	operator: 28 operands: 19
17	Operation	operator: 20 operands: 21
18	Variable
19	ExprTuple	22, 32
20	Literal
21	ExprTuple	23, 24
22	Operation	operator: 25 operands: 26
23	Operation	operator: 28 operands: 27
24	Operation	operator: 28 operands: 29
25	Literal
26	ExprTuple	30, 31
27	ExprTuple	37, 32
28	Literal
29	ExprTuple	39, 32
30	Operation	operator: 34 operands: 33
31	Operation	operator: 34 operands: 35
32	Variable
33	ExprTuple	36, 37
34	Literal
35	ExprTuple	38, 39
36	Variable
37	Variable
38	Variable
39	Variable