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 A, B, C, Conditional, ExprRange, IndexedVar, Lambda, Variable, 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, InSet
from proveit.numbers import one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Lambda([A_1_to_l, B_1_to_m, C_1_to_n], Conditional(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), And(ExprRange(sub_expr1, InSet(IndexedVar(A, sub_expr1), Boolean), one, l), ExprRange(sub_expr1, InSet(IndexedVar(B, sub_expr1), Boolean), one, m), ExprRange(sub_expr1, InSet(IndexedVar(C, sub_expr1), Boolean), one, n))))

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(A_{1}, A_{2}, \ldots, A_{l}, B_{1}, B_{2}, \ldots, B_{m}, C_{1}, C_{2}, \ldots, C_{n}\right) \mapsto \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} \textrm{ if } \left(A_{1} \in \mathbb{B}\right) ,  \left(A_{2} \in \mathbb{B}\right) ,  \ldots ,  \left(A_{l} \in \mathbb{B}\right), \left(B_{1} \in \mathbb{B}\right) ,  \left(B_{2} \in \mathbb{B}\right) ,  \ldots ,  \left(B_{m} \in \mathbb{B}\right), \left(C_{1} \in \mathbb{B}\right) ,  \left(C_{2} \in \mathbb{B}\right) ,  \ldots ,  \left(C_{n} \in \mathbb{B}\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: 12 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 4 operands: 5
3	Operation	operator: 25 operands: 6
4	Literal
5	ExprTuple	7, 8
6	ExprTuple	9, 10, 11
7	Operation	operator: 25 operands: 12
8	Operation	operator: 25 operands: 13
9	ExprRange	lambda_map: 14 start_index: 38 end_index: 24
10	ExprRange	lambda_map: 15 start_index: 38 end_index: 39
11	ExprRange	lambda_map: 16 start_index: 38 end_index: 28
12	ExprTuple	17, 33, 19
13	ExprTuple	17, 18, 19
14	Lambda	parameter: 45 body: 20
15	Lambda	parameter: 45 body: 21
16	Lambda	parameter: 45 body: 22
17	ExprRange	lambda_map: 23 start_index: 38 end_index: 24
18	Operation	operator: 25 operands: 26
19	ExprRange	lambda_map: 27 start_index: 38 end_index: 28
20	Operation	operator: 31 operands: 29
21	Operation	operator: 31 operands: 30
22	Operation	operator: 31 operands: 32
23	Lambda	parameter: 45 body: 34
24	Variable
25	Literal
26	ExprTuple	33
27	Lambda	parameter: 45 body: 35
28	Variable
29	ExprTuple	34, 36
30	ExprTuple	42, 36
31	Literal
32	ExprTuple	35, 36
33	ExprRange	lambda_map: 37 start_index: 38 end_index: 39
34	IndexedVar	variable: 40 index: 45
35	IndexedVar	variable: 41 index: 45
36	Literal
37	Lambda	parameter: 45 body: 42
38	Literal
39	Variable
40	Variable
41	Variable
42	IndexedVar	variable: 43 index: 45
43	Variable
44	ExprTuple	45
45	Variable