Expression of type Lambda

from the theory of proveit.logic.booleans.conjunction

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, l, m, n
from proveit.core_expr_types import A_1_to_l, B_1_to_m, C_1_to_n
from proveit.logic import And, Boolean, Equals, Forall, InSet
from proveit.numbers import Natural

# build up the expression from sub-expressions
expr = Lambda([l, m, n], Conditional(Forall(instance_param_or_params = [A_1_to_l, B_1_to_m, C_1_to_n], instance_expr = Equals(And(A_1_to_l, B_1_to_m, C_1_to_n), And(A_1_to_l, And(B_1_to_m), C_1_to_n)).with_wrapping_at(2), domain = Boolean), And(InSet(l, Natural), InSet(m, Natural), InSet(n, 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(l, m, n\right) \mapsto \left\{\forall_{A_{1}, A_{2}, \ldots, A_{l}, B_{1}, B_{2}, \ldots, B_{m}, C_{1}, C_{2}, \ldots, C_{n} \in \mathbb{B}}~\left(\begin{array}{c} \begin{array}{l} \left(A_{1} \land  A_{2} \land  \ldots \land  A_{l}\land B_{1} \land  B_{2} \land  \ldots \land  B_{m}\land C_{1} \land  C_{2} \land  \ldots \land  C_{n}\right) =  \\ \left(A_{1} \land  A_{2} \land  \ldots \land  A_{l} \land \left(B_{1} \land  B_{2} \land  \ldots \land  B_{m}\right)\land C_{1} \land  C_{2} \land  \ldots \land  C_{n}\right) \end{array} \end{array}\right) \textrm{ if } l \in \mathbb{N} ,  m \in \mathbb{N} ,  n \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	39, 54, 43
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 8
4	Operation	operator: 40 operands: 7
5	Literal
6	ExprTuple	8
7	ExprTuple	9, 10, 11
8	Lambda	parameters: 27 body: 12
9	Operation	operator: 46 operands: 13
10	Operation	operator: 46 operands: 14
11	Operation	operator: 46 operands: 15
12	Conditional	value: 16 condition: 17
13	ExprTuple	39, 18
14	ExprTuple	54, 18
15	ExprTuple	43, 18
16	Operation	operator: 19 operands: 20
17	Operation	operator: 40 operands: 21
18	Literal
19	Literal
20	ExprTuple	22, 23
21	ExprTuple	24, 25, 26
22	Operation	operator: 40 operands: 27
23	Operation	operator: 40 operands: 28
24	ExprRange	lambda_map: 29 start_index: 53 end_index: 39
25	ExprRange	lambda_map: 30 start_index: 53 end_index: 54
26	ExprRange	lambda_map: 31 start_index: 53 end_index: 43
27	ExprTuple	32, 48, 34
28	ExprTuple	32, 33, 34
29	Lambda	parameter: 60 body: 35
30	Lambda	parameter: 60 body: 36
31	Lambda	parameter: 60 body: 37
32	ExprRange	lambda_map: 38 start_index: 53 end_index: 39
33	Operation	operator: 40 operands: 41
34	ExprRange	lambda_map: 42 start_index: 53 end_index: 43
35	Operation	operator: 46 operands: 44
36	Operation	operator: 46 operands: 45
37	Operation	operator: 46 operands: 47
38	Lambda	parameter: 60 body: 49
39	Variable
40	Literal
41	ExprTuple	48
42	Lambda	parameter: 60 body: 50
43	Variable
44	ExprTuple	49, 51
45	ExprTuple	57, 51
46	Literal
47	ExprTuple	50, 51
48	ExprRange	lambda_map: 52 start_index: 53 end_index: 54
49	IndexedVar	variable: 55 index: 60
50	IndexedVar	variable: 56 index: 60
51	Literal
52	Lambda	parameter: 60 body: 57
53	Literal
54	Variable
55	Variable
56	Variable
57	IndexedVar	variable: 58 index: 60
58	Variable
59	ExprTuple	60
60	Variable