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, v
from proveit.linear_algebra import ScalarMult, VecSpaces
from proveit.logic import Equals, Forall, InSet
from proveit.numbers import one

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(K, Conditional(Forall(instance_param_or_params = [v, V], instance_expr = Equals(ScalarMult(one, v), v), domains = [V, VecSpaces(K)]), InSet(one, 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 \in V, V \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)}~\left(\left(1 \cdot v\right) = v\right) \textrm{ if } 1 \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: 31 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 8
4	Operation	operator: 21 operands: 7
5	Literal
6	ExprTuple	8
7	ExprTuple	25, 31
8	Lambda	parameters: 22 body: 9
9	Conditional	value: 10 condition: 11
10	Operation	operator: 12 operands: 13
11	Operation	operator: 14 operands: 15
12	Literal
13	ExprTuple	16, 26
14	Literal
15	ExprTuple	17, 18
16	Operation	operator: 19 operands: 20
17	Operation	operator: 21 operands: 22
18	Operation	operator: 23 operands: 24
19	Literal
20	ExprTuple	25, 26
21	Literal
22	ExprTuple	26, 27
23	Literal
24	ExprTuple	27, 28
25	Literal
26	Variable
27	Variable
28	Operation	operator: 29 operand: 31
29	Literal
30	ExprTuple	31
31	Variable