Expression of type Lambda

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, 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 = 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())

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..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 29 body: 2
1	ExprTuple	29
2	Conditional	value: 3 condition: 4
3	Operation	operator: 16 operand: 8
4	Operation	operator: 6 operands: 7
5	ExprTuple	8
6	Literal
7	ExprTuple	29, 9
8	Lambda	parameter: 32 body: 11
9	Operation	operator: 12 operand: 20
10	ExprTuple	32
11	Conditional	value: 14 condition: 15
12	Literal
13	ExprTuple	20
14	Operation	operator: 16 operand: 19
15	Operation	operator: 26 operands: 18
16	Literal
17	ExprTuple	19
18	ExprTuple	32, 20
19	Lambda	parameter: 33 body: 22
20	Variable
21	ExprTuple	33
22	Conditional	value: 23 condition: 24
23	Operation	operator: 26 operands: 25
24	Operation	operator: 26 operands: 27
25	ExprTuple	28, 29
26	Literal
27	ExprTuple	33, 29
28	Operation	operator: 30 operands: 31
29	Variable
30	Literal
31	ExprTuple	32, 33
32	Variable
33	Variable