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, Or
from proveit.numbers import one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = IndexedVar(A, sub_expr1)
sub_expr3 = IndexedVar(B, sub_expr1)
expr = Lambda([A_1_to_m, B_1_to_m], Conditional(Or(B_1_to_m), And(ExprRange(sub_expr1, InSet(sub_expr2, Boolean), one, m), ExprRange(sub_expr1, InSet(sub_expr3, Boolean), one, m), Or(A_1_to_m), ExprRange(sub_expr1, Implies(sub_expr2, sub_expr3), 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\{B_{1} \lor  B_{2} \lor  \ldots \lor  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) ,  A_{1} \lor  A_{2} \lor  \ldots \lor  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	21, 8
2	Conditional	value: 3 condition: 4
3	Operation	operator: 16 operands: 5
4	Operation	operator: 6 operands: 7
5	ExprTuple	8
6	Literal
7	ExprTuple	9, 10, 11, 12
8	ExprRange	lambda_map: 13 start_index: 27 end_index: 28
9	ExprRange	lambda_map: 14 start_index: 27 end_index: 28
10	ExprRange	lambda_map: 15 start_index: 27 end_index: 28
11	Operation	operator: 16 operands: 17
12	ExprRange	lambda_map: 18 start_index: 27 end_index: 28
13	Lambda	parameter: 37 body: 33
14	Lambda	parameter: 37 body: 19
15	Lambda	parameter: 37 body: 20
16	Literal
17	ExprTuple	21
18	Lambda	parameter: 37 body: 22
19	Operation	operator: 24 operands: 23
20	Operation	operator: 24 operands: 25
21	ExprRange	lambda_map: 26 start_index: 27 end_index: 28
22	Operation	operator: 29 operands: 30
23	ExprTuple	32, 31
24	Literal
25	ExprTuple	33, 31
26	Lambda	parameter: 37 body: 32
27	Literal
28	Variable
29	Literal
30	ExprTuple	32, 33
31	Literal
32	IndexedVar	variable: 34 index: 37
33	IndexedVar	variable: 35 index: 37
34	Variable
35	Variable
36	ExprTuple	37
37	Variable