Expression of type Lambda

from the theory of proveit.numbers.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, Lambda, i, j
from proveit.core_expr_types import a_1_to_i, b_1_to_j
from proveit.logic import And, Equals, Forall, InSet
from proveit.numbers import Add, Complex, Natural, zero

# build up the expression from sub-expressions
expr = Lambda([i, j], Conditional(Forall(instance_param_or_params = [a_1_to_i, b_1_to_j], instance_expr = Equals(Add(a_1_to_i, zero, b_1_to_j), Add(a_1_to_i, b_1_to_j)), domain = Complex), And(InSet(i, Natural), InSet(j, Natural))))

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(i, j\right) \mapsto \left\{\forall_{a_{1}, a_{2}, \ldots, a_{i}, b_{1}, b_{2}, \ldots, b_{j} \in \mathbb{C}}~\left(\left(a_{1} +  a_{2} +  \ldots +  a_{i} + 0+ b_{1} +  b_{2} +  \ldots +  b_{j}\right) = \left(a_{1} +  a_{2} +  \ldots +  a_{i}+ b_{1} +  b_{2} +  \ldots +  b_{j}\right)\right) \textrm{ if } i \in \mathbb{N} ,  j \in \mathbb{N}\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	36, 39
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 8
4	Operation	operator: 19 operands: 7
5	Literal
6	ExprTuple	8
7	ExprTuple	9, 10
8	Lambda	parameters: 27 body: 11
9	Operation	operator: 41 operands: 12
10	Operation	operator: 41 operands: 13
11	Conditional	value: 14 condition: 15
12	ExprTuple	36, 16
13	ExprTuple	39, 16
14	Operation	operator: 17 operands: 18
15	Operation	operator: 19 operands: 20
16	Literal
17	Literal
18	ExprTuple	21, 22
19	Literal
20	ExprTuple	23, 24
21	Operation	operator: 26 operands: 25
22	Operation	operator: 26 operands: 27
23	ExprRange	lambda_map: 28 start_index: 38 end_index: 36
24	ExprRange	lambda_map: 29 start_index: 38 end_index: 39
25	ExprTuple	31, 30, 32
26	Literal
27	ExprTuple	31, 32
28	Lambda	parameter: 49 body: 33
29	Lambda	parameter: 49 body: 34
30	Literal
31	ExprRange	lambda_map: 35 start_index: 38 end_index: 36
32	ExprRange	lambda_map: 37 start_index: 38 end_index: 39
33	Operation	operator: 41 operands: 40
34	Operation	operator: 41 operands: 42
35	Lambda	parameter: 49 body: 43
36	Variable
37	Lambda	parameter: 49 body: 44
38	Literal
39	Variable
40	ExprTuple	43, 45
41	Literal
42	ExprTuple	44, 45
43	IndexedVar	variable: 46 index: 49
44	IndexedVar	variable: 47 index: 49
45	Literal
46	Variable
47	Variable
48	ExprTuple	49
49	Variable