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

# build up the expression from sub-expressions
expr = Lambda(K, Forall(instance_param_or_params = [V], instance_expr = 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), domain = 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())

K \mapsto \left[\forall_{V \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)}~\left[\forall_{a \in K}~\left[\forall_{x \in V}~\left(\left(a \cdot x\right) \in V\right)\right]\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: 23 body: 1
1	Operation	operator: 19 operand: 3
2	ExprTuple	3
3	Lambda	parameter: 32 body: 5
4	ExprTuple	32
5	Conditional	value: 6 condition: 7
6	Operation	operator: 19 operand: 11
7	Operation	operator: 9 operands: 10
8	ExprTuple	11
9	Literal
10	ExprTuple	32, 12
11	Lambda	parameter: 35 body: 14
12	Operation	operator: 15 operand: 23
13	ExprTuple	35
14	Conditional	value: 17 condition: 18
15	Literal
16	ExprTuple	23
17	Operation	operator: 19 operand: 22
18	Operation	operator: 29 operands: 21
19	Literal
20	ExprTuple	22
21	ExprTuple	35, 23
22	Lambda	parameter: 36 body: 25
23	Variable
24	ExprTuple	36
25	Conditional	value: 26 condition: 27
26	Operation	operator: 29 operands: 28
27	Operation	operator: 29 operands: 30
28	ExprTuple	31, 32
29	Literal
30	ExprTuple	36, 32
31	Operation	operator: 33 operands: 34
32	Variable
33	Literal
34	ExprTuple	35, 36
35	Variable
36	Variable