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(Neg(Mult(a_1_to_i, Neg(b), c_1_to_j)), 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(-\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)\right) = \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) \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	44, 49
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: 37 operands: 12
10	Operation	operator: 37 operands: 13
11	Conditional	value: 14 condition: 15
12	ExprTuple	44, 16
13	ExprTuple	49, 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: 45 operand: 31
22	Operation	operator: 34 operands: 27
23	ExprRange	lambda_map: 28 start_index: 48 end_index: 44
24	Operation	operator: 37 operands: 29
25	ExprRange	lambda_map: 30 start_index: 48 end_index: 49
26	ExprTuple	31
27	ExprTuple	39, 51, 41
28	Lambda	parameter: 56 body: 32
29	ExprTuple	51, 42
30	Lambda	parameter: 56 body: 33
31	Operation	operator: 34 operands: 35
32	Operation	operator: 37 operands: 36
33	Operation	operator: 37 operands: 38
34	Literal
35	ExprTuple	39, 40, 41
36	ExprTuple	50, 42
37	Literal
38	ExprTuple	52, 42
39	ExprRange	lambda_map: 43 start_index: 48 end_index: 44
40	Operation	operator: 45 operand: 51
41	ExprRange	lambda_map: 47 start_index: 48 end_index: 49
42	Literal
43	Lambda	parameter: 56 body: 50
44	Variable
45	Literal
46	ExprTuple	51
47	Lambda	parameter: 56 body: 52
48	Literal
49	Variable
50	IndexedVar	variable: 53 index: 56
51	Variable
52	IndexedVar	variable: 54 index: 56
53	Variable
54	Variable
55	ExprTuple	56
56	Variable