Expression of type Lambda

from the theory of proveit.numbers.summation

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, Function, Lambda, f, g, k, l, m, n
from proveit.logic import And, Equals, Forall, Implies, InSet
from proveit.numbers import Integer, Interval, Sum

# build up the expression from sub-expressions
sub_expr1 = [k]
sub_expr2 = [l]
sub_expr3 = Interval(m, n)
expr = Lambda([m, n], Conditional(Implies(Forall(instance_param_or_params = sub_expr1, instance_expr = Equals(Function(f, sub_expr1), Function(g, sub_expr1)), domain = sub_expr3), Equals(Sum(index_or_indices = sub_expr2, summand = Function(f, sub_expr2), domain = sub_expr3), Sum(index_or_indices = sub_expr2, summand = Function(g, sub_expr2), domain = sub_expr3))), And(InSet(m, Integer), InSet(n, Integer))))

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())

\left(m, n\right) \mapsto \left\{\left[\forall_{k \in \{m~\ldotp \ldotp~n\}}~\left(f\left(k\right) = g\left(k\right)\right)\right] \Rightarrow \left(\left(\sum_{l = m}^{n} f\left(l\right)\right) = \left(\sum_{l = m}^{n} g\left(l\right)\right)\right) \textrm{ if } m \in \mathbb{Z} ,  n \in \mathbb{Z}\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 49 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 4 operands: 5
3	Operation	operator: 6 operands: 7
4	Literal
5	ExprTuple	8, 9
6	Literal
7	ExprTuple	10, 11
8	Operation	operator: 12 operand: 17
9	Operation	operator: 29 operands: 14
10	Operation	operator: 43 operands: 15
11	Operation	operator: 43 operands: 16
12	Literal
13	ExprTuple	17
14	ExprTuple	18, 19
15	ExprTuple	50, 20
16	ExprTuple	51, 20
17	Lambda	parameter: 45 body: 21
18	Operation	operator: 23 operand: 27
19	Operation	operator: 23 operand: 28
20	Literal
21	Conditional	value: 25 condition: 26
22	ExprTuple	27
23	Literal
24	ExprTuple	28
25	Operation	operator: 29 operands: 30
26	Operation	operator: 43 operands: 31
27	Lambda	parameter: 46 body: 32
28	Lambda	parameter: 46 body: 33
29	Literal
30	ExprTuple	34, 35
31	ExprTuple	45, 47
32	Conditional	value: 36 condition: 38
33	Conditional	value: 37 condition: 38
34	Operation	operator: 40 operand: 45
35	Operation	operator: 41 operand: 45
36	Operation	operator: 40 operand: 46
37	Operation	operator: 41 operand: 46
38	Operation	operator: 43 operands: 44
39	ExprTuple	45
40	Variable
41	Variable
42	ExprTuple	46
43	Literal
44	ExprTuple	46, 47
45	Variable
46	Variable
47	Operation	operator: 48 operands: 49
48	Literal
49	ExprTuple	50, 51
50	Variable
51	Variable