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, D, ExprRange, IndexedVar, Lambda, Variable, l, m, n
from proveit.core_expr_types import A_1_to_l, C_1_to_m, D_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, C_1_to_m, D_1_to_n], Conditional(Equals(And(A_1_to_l, B, C_1_to_m, D_1_to_n), And(A_1_to_l, C_1_to_m, B, D_1_to_n)).with_wrapping_at(2), And(ExprRange(sub_expr1, InSet(IndexedVar(A, sub_expr1), Boolean), one, l), InSet(B, Boolean), ExprRange(sub_expr1, InSet(IndexedVar(C, sub_expr1), Boolean), one, m), ExprRange(sub_expr1, InSet(IndexedVar(D, 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, C_{1}, C_{2}, \ldots, C_{m}, D_{1}, D_{2}, \ldots, D_{n}\right) \mapsto \left\{\begin{array}{c} \begin{array}{l} \left(A_{1} \land  A_{2} \land  \ldots \land  A_{l} \land B\land C_{1} \land  C_{2} \land  \ldots \land  C_{m}\land D_{1} \land  D_{2} \land  \ldots \land  D_{n}\right) =  \\ \left(A_{1} \land  A_{2} \land  \ldots \land  A_{l}\land C_{1} \land  C_{2} \land  \ldots \land  C_{m} \land B\land D_{1} \land  D_{2} \land  \ldots \land  D_{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) ,  B \in \mathbb{B}, \left(C_{1} \in \mathbb{B}\right) ,  \left(C_{2} \in \mathbb{B}\right) ,  \ldots ,  \left(C_{m} \in \mathbb{B}\right), \left(D_{1} \in \mathbb{B}\right) ,  \left(D_{2} \in \mathbb{B}\right) ,  \ldots ,  \left(D_{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: 13 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 4 operands: 5
3	Operation	operator: 14 operands: 6
4	Literal
5	ExprTuple	7, 8
6	ExprTuple	9, 10, 11, 12
7	Operation	operator: 14 operands: 13
8	Operation	operator: 14 operands: 15
9	ExprRange	lambda_map: 16 start_index: 32 end_index: 28
10	Operation	operator: 36 operands: 17
11	ExprRange	lambda_map: 18 start_index: 32 end_index: 30
12	ExprRange	lambda_map: 19 start_index: 32 end_index: 33
13	ExprTuple	20, 24, 21, 22
14	Literal
15	ExprTuple	20, 21, 24, 22
16	Lambda	parameter: 46 body: 23
17	ExprTuple	24, 41
18	Lambda	parameter: 46 body: 25
19	Lambda	parameter: 46 body: 26
20	ExprRange	lambda_map: 27 start_index: 32 end_index: 28
21	ExprRange	lambda_map: 29 start_index: 32 end_index: 30
22	ExprRange	lambda_map: 31 start_index: 32 end_index: 33
23	Operation	operator: 36 operands: 34
24	Variable
25	Operation	operator: 36 operands: 35
26	Operation	operator: 36 operands: 37
27	Lambda	parameter: 46 body: 38
28	Variable
29	Lambda	parameter: 46 body: 39
30	Variable
31	Lambda	parameter: 46 body: 40
32	Literal
33	Variable
34	ExprTuple	38, 41
35	ExprTuple	39, 41
36	Literal
37	ExprTuple	40, 41
38	IndexedVar	variable: 42 index: 46
39	IndexedVar	variable: 43 index: 46
40	IndexedVar	variable: 44 index: 46
41	Literal
42	Variable
43	Variable
44	Variable
45	ExprTuple	46
46	Variable