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 Function, Lambda, f, g, k, l, m, n
from proveit.logic import Equals, Forall, Implies
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([f, g], Forall(instance_param_or_params = [m, n], instance_expr = 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))), domain = 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(f, g\right) \mapsto \left[\forall_{m, n \in \mathbb{Z}}~\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)\right)\right]

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 1 body: 2
1	ExprTuple	44, 45
2	Operation	operator: 16 operand: 4
3	ExprTuple	4
4	Lambda	parameters: 53 body: 5
5	Conditional	value: 6 condition: 7
6	Operation	operator: 8 operands: 9
7	Operation	operator: 10 operands: 11
8	Literal
9	ExprTuple	12, 13
10	Literal
11	ExprTuple	14, 15
12	Operation	operator: 16 operand: 21
13	Operation	operator: 33 operands: 18
14	Operation	operator: 47 operands: 19
15	Operation	operator: 47 operands: 20
16	Literal
17	ExprTuple	21
18	ExprTuple	22, 23
19	ExprTuple	54, 24
20	ExprTuple	55, 24
21	Lambda	parameter: 49 body: 25
22	Operation	operator: 27 operand: 31
23	Operation	operator: 27 operand: 32
24	Literal
25	Conditional	value: 29 condition: 30
26	ExprTuple	31
27	Literal
28	ExprTuple	32
29	Operation	operator: 33 operands: 34
30	Operation	operator: 47 operands: 35
31	Lambda	parameter: 50 body: 36
32	Lambda	parameter: 50 body: 37
33	Literal
34	ExprTuple	38, 39
35	ExprTuple	49, 51
36	Conditional	value: 40 condition: 42
37	Conditional	value: 41 condition: 42
38	Operation	operator: 44 operand: 49
39	Operation	operator: 45 operand: 49
40	Operation	operator: 44 operand: 50
41	Operation	operator: 45 operand: 50
42	Operation	operator: 47 operands: 48
43	ExprTuple	49
44	Variable
45	Variable
46	ExprTuple	50
47	Literal
48	ExprTuple	50, 51
49	Variable
50	Variable
51	Operation	operator: 52 operands: 53
52	Literal
53	ExprTuple	54, 55
54	Variable
55	Variable