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
from proveit.logic import Forall, InSet

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(a, Conditional(Forall(instance_param_or_params = [x], instance_expr = InSet(ScalarMult(a, x), V), domain = V), InSet(a, 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(a \mapsto \left\{\forall_{x \in V}~\left(\left(a \cdot x\right) \in V\right) \textrm{ if } a \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	parameter: 22 body: 3
2	ExprTuple	22
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 9
5	Operation	operator: 16 operands: 8
6	Literal
7	ExprTuple	9
8	ExprTuple	22, 10
9	Lambda	parameter: 23 body: 12
10	Variable
11	ExprTuple	23
12	Conditional	value: 13 condition: 14
13	Operation	operator: 16 operands: 15
14	Operation	operator: 16 operands: 17
15	ExprTuple	18, 19
16	Literal
17	ExprTuple	23, 19
18	Operation	operator: 20 operands: 21
19	Variable
20	Literal
21	ExprTuple	22, 23
22	Variable
23	Variable