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, b, x, y
from proveit.linear_algebra import VecSpaces, binary_lin_comb_ax_by
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, b], instance_expr = Forall(instance_param_or_params = [x, y], instance_expr = InSet(binary_lin_comb_ax_by, 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, b \in K}~\left[\forall_{x, y \in V}~\left(\left(\left(a \cdot x\right) + \left(b \cdot y\right)\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: 31 body: 1
1	Operation	operator: 19 operand: 3
2	ExprTuple	3
3	Lambda	parameter: 45 body: 5
4	ExprTuple	45
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	45, 12
11	Lambda	parameters: 13 body: 14
12	Operation	operator: 15 operand: 31
13	ExprTuple	49, 51
14	Conditional	value: 17 condition: 18
15	Literal
16	ExprTuple	31
17	Operation	operator: 19 operand: 22
18	Operation	operator: 33 operands: 21
19	Literal
20	ExprTuple	22
21	ExprTuple	23, 24
22	Lambda	parameters: 25 body: 26
23	Operation	operator: 41 operands: 27
24	Operation	operator: 41 operands: 28
25	ExprTuple	50, 52
26	Conditional	value: 29 condition: 30
27	ExprTuple	49, 31
28	ExprTuple	51, 31
29	Operation	operator: 41 operands: 32
30	Operation	operator: 33 operands: 34
31	Variable
32	ExprTuple	35, 45
33	Literal
34	ExprTuple	36, 37
35	Operation	operator: 38 operands: 39
36	Operation	operator: 41 operands: 40
37	Operation	operator: 41 operands: 42
38	Literal
39	ExprTuple	43, 44
40	ExprTuple	50, 45
41	Literal
42	ExprTuple	52, 45
43	Operation	operator: 47 operands: 46
44	Operation	operator: 47 operands: 48
45	Variable
46	ExprTuple	49, 50
47	Literal
48	ExprTuple	51, 52
49	Variable
50	Variable
51	Variable
52	Variable