Expression of type Lambda

from the theory of proveit.numbers.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, Lambda, b, i, j
from proveit.core_expr_types import a_1_to_i, c_1_to_j
from proveit.logic import And, Equals, Forall, InSet
from proveit.numbers import Complex, Mult, Natural, Neg

# build up the expression from sub-expressions
expr = Lambda([i, j], Conditional(Forall(instance_param_or_params = [a_1_to_i, b, c_1_to_j], instance_expr = Equals(Mult(a_1_to_i, Neg(b), c_1_to_j), Neg(Mult(a_1_to_i, b, c_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, c_{1}, c_{2}, \ldots, c_{j} \in \mathbb{C}}~\left(\left(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{i} \cdot \left(-b\right)\cdot c_{1} \cdot  c_{2} \cdot  \ldots \cdot  c_{j}\right) = \left(-\left(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{i} \cdot b\cdot c_{1} \cdot  c_{2} \cdot  \ldots \cdot  c_{j}\right)\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	47, 50
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: 38 body: 11
9	Operation	operator: 40 operands: 12
10	Operation	operator: 40 operands: 13
11	Conditional	value: 14 condition: 15
12	ExprTuple	47, 16
13	ExprTuple	50, 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, 25
21	Operation	operator: 37 operands: 26
22	Operation	operator: 35 operand: 32
23	ExprRange	lambda_map: 28 start_index: 49 end_index: 47
24	Operation	operator: 40 operands: 29
25	ExprRange	lambda_map: 30 start_index: 49 end_index: 50
26	ExprTuple	42, 31, 44
27	ExprTuple	32
28	Lambda	parameter: 56 body: 33
29	ExprTuple	43, 45
30	Lambda	parameter: 56 body: 34
31	Operation	operator: 35 operand: 43
32	Operation	operator: 37 operands: 38
33	Operation	operator: 40 operands: 39
34	Operation	operator: 40 operands: 41
35	Literal
36	ExprTuple	43
37	Literal
38	ExprTuple	42, 43, 44
39	ExprTuple	51, 45
40	Literal
41	ExprTuple	52, 45
42	ExprRange	lambda_map: 46 start_index: 49 end_index: 47
43	Variable
44	ExprRange	lambda_map: 48 start_index: 49 end_index: 50
45	Literal
46	Lambda	parameter: 56 body: 51
47	Variable
48	Lambda	parameter: 56 body: 52
49	Literal
50	Variable
51	IndexedVar	variable: 53 index: 56
52	IndexedVar	variable: 54 index: 56
53	Variable
54	Variable
55	ExprTuple	56
56	Variable