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, b, x, y
from proveit.linear_algebra import VecSpaces, binary_lin_comb_ax_by
from proveit.logic import Forall, InClass, InSet

# build up the expression from sub-expressions
expr = Lambda(V, Conditional(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), 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, 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] \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: 42 body: 2
1	ExprTuple	42
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	42, 9
8	Lambda	parameters: 10 body: 11
9	Operation	operator: 12 operand: 28
10	ExprTuple	46, 48
11	Conditional	value: 14 condition: 15
12	Literal
13	ExprTuple	28
14	Operation	operator: 16 operand: 19
15	Operation	operator: 30 operands: 18
16	Literal
17	ExprTuple	19
18	ExprTuple	20, 21
19	Lambda	parameters: 22 body: 23
20	Operation	operator: 38 operands: 24
21	Operation	operator: 38 operands: 25
22	ExprTuple	47, 49
23	Conditional	value: 26 condition: 27
24	ExprTuple	46, 28
25	ExprTuple	48, 28
26	Operation	operator: 38 operands: 29
27	Operation	operator: 30 operands: 31
28	Variable
29	ExprTuple	32, 42
30	Literal
31	ExprTuple	33, 34
32	Operation	operator: 35 operands: 36
33	Operation	operator: 38 operands: 37
34	Operation	operator: 38 operands: 39
35	Literal
36	ExprTuple	40, 41
37	ExprTuple	47, 42
38	Literal
39	ExprTuple	49, 42
40	Operation	operator: 44 operands: 43
41	Operation	operator: 44 operands: 45
42	Variable
43	ExprTuple	46, 47
44	Literal
45	ExprTuple	48, 49
46	Variable
47	Variable
48	Variable
49	Variable