Expression of type Lambda

from the theory of proveit.logic.booleans.disjunction

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, Conditional, ExprRange, IndexedVar, Lambda, Variable, m
from proveit.core_expr_types import A_1_to_m, B_1_to_m
from proveit.logic import And, Boolean, Implies, InSet, Not, Or
from proveit.numbers import one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = IndexedVar(B, sub_expr1)
sub_expr3 = IndexedVar(A, sub_expr1)
expr = Lambda([A_1_to_m, B_1_to_m], Conditional(Or(ExprRange(sub_expr1, Not(sub_expr2), one, m)), And(ExprRange(sub_expr1, InSet(sub_expr3, Boolean), one, m), ExprRange(sub_expr1, InSet(sub_expr2, Boolean), one, m), Or(ExprRange(sub_expr1, Not(sub_expr3), one, m)), ExprRange(sub_expr1, Implies(sub_expr3, sub_expr2), one, m))))

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_{m}, B_{1}, B_{2}, \ldots, B_{m}\right) \mapsto \left\{(\lnot B_{1}) \lor  (\lnot B_{2}) \lor  \ldots \lor  (\lnot B_{m}) \textrm{ if } \left(A_{1} \in \mathbb{B}\right) ,  \left(A_{2} \in \mathbb{B}\right) ,  \ldots ,  \left(A_{m} \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) ,  (\lnot A_{1}) \lor  (\lnot A_{2}) \lor  \ldots \lor  (\lnot A_{m}), \left(A_{1} \Rightarrow B_{1}\right) ,  \left(A_{2} \Rightarrow B_{2}\right) ,  \ldots ,  \left(A_{m} \Rightarrow B_{m}\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: 1 body: 2
1	ExprTuple	3, 4
2	Conditional	value: 5 condition: 6
3	ExprRange	lambda_map: 7 start_index: 33 end_index: 34
4	ExprRange	lambda_map: 8 start_index: 33 end_index: 34
5	Operation	operator: 20 operands: 9
6	Operation	operator: 10 operands: 11
7	Lambda	parameter: 46 body: 43
8	Lambda	parameter: 46 body: 39
9	ExprTuple	12
10	Literal
11	ExprTuple	13, 14, 15, 16
12	ExprRange	lambda_map: 17 start_index: 33 end_index: 34
13	ExprRange	lambda_map: 18 start_index: 33 end_index: 34
14	ExprRange	lambda_map: 19 start_index: 33 end_index: 34
15	Operation	operator: 20 operands: 21
16	ExprRange	lambda_map: 22 start_index: 33 end_index: 34
17	Lambda	parameter: 46 body: 23
18	Lambda	parameter: 46 body: 24
19	Lambda	parameter: 46 body: 25
20	Literal
21	ExprTuple	26
22	Lambda	parameter: 46 body: 27
23	Operation	operator: 40 operand: 39
24	Operation	operator: 30 operands: 29
25	Operation	operator: 30 operands: 31
26	ExprRange	lambda_map: 32 start_index: 33 end_index: 34
27	Operation	operator: 35 operands: 36
28	ExprTuple	39
29	ExprTuple	43, 37
30	Literal
31	ExprTuple	39, 37
32	Lambda	parameter: 46 body: 38
33	Literal
34	Variable
35	Literal
36	ExprTuple	43, 39
37	Literal
38	Operation	operator: 40 operand: 43
39	IndexedVar	variable: 42 index: 46
40	Literal
41	ExprTuple	43
42	Variable
43	IndexedVar	variable: 44 index: 46
44	Variable
45	ExprTuple	46
46	Variable