Expression of type Lambda

from the theory of proveit.linear_algebra.addition

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, i, j, k, v
from proveit.linear_algebra import ScalarMult, VecSpaces, VecSum
from proveit.logic import Equals, Forall, InClass
from proveit.numbers import Add, Interval, one, subtract

# build up the expression from sub-expressions
expr = Lambda(V, Conditional(Forall(instance_param_or_params = [v], instance_expr = Equals(VecSum(index_or_indices = [i], summand = v, domain = Interval(j, k)), ScalarMult(Add(subtract(k, j), one), v)), domain = V), 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_{v \in V}~\left(\left(\sum_{i=j}^{k} v\right) = \left(\left(\left(k - j\right) + 1\right) \cdot 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: 23 body: 2
1	ExprTuple	23
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 9
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9
7	Literal
8	ExprTuple	23, 10
9	Lambda	parameter: 33 body: 12
10	Operation	operator: 13 operand: 17
11	ExprTuple	33
12	Conditional	value: 15 condition: 16
13	Literal
14	ExprTuple	17
15	Operation	operator: 18 operands: 19
16	Operation	operator: 37 operands: 20
17	Variable
18	Literal
19	ExprTuple	21, 22
20	ExprTuple	33, 23
21	Operation	operator: 24 operand: 28
22	Operation	operator: 26 operands: 27
23	Variable
24	Literal
25	ExprTuple	28
26	Literal
27	ExprTuple	29, 33
28	Lambda	parameter: 41 body: 31
29	Operation	operator: 39 operands: 32
30	ExprTuple	41
31	Conditional	value: 33 condition: 34
32	ExprTuple	35, 36
33	Variable
34	Operation	operator: 37 operands: 38
35	Operation	operator: 39 operands: 40
36	Literal
37	Literal
38	ExprTuple	41, 42
39	Literal
40	ExprTuple	48, 43
41	Variable
42	Operation	operator: 44 operands: 45
43	Operation	operator: 46 operand: 49
44	Literal
45	ExprTuple	49, 48
46	Literal
47	ExprTuple	49
48	Variable
49	Variable