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, C, Conditional, ExprRange, IndexedVar, Lambda, Variable, m, n
from proveit.core_expr_types import A_1_to_m, C_1_to_n
from proveit.logic import And, Boolean, InSet, Or
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_m, B, C_1_to_n], Conditional(Or(A_1_to_m, B, C_1_to_n), And(ExprRange(sub_expr1, InSet(IndexedVar(A, sub_expr1), Boolean), one, m), InSet(B, Boolean), ExprRange(sub_expr1, InSet(IndexedVar(C, sub_expr1), Boolean), one, n), B)))

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, C_{1}, C_{2}, \ldots, C_{n}\right) \mapsto \left\{A_{1} \lor  A_{2} \lor  \ldots \lor  A_{m} \lor B\lor C_{1} \lor  C_{2} \lor  \ldots \lor  C_{n} \textrm{ if } \left(A_{1} \in \mathbb{B}\right) ,  \left(A_{2} \in \mathbb{B}\right) ,  \ldots ,  \left(A_{m} \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_{n} \in \mathbb{B}\right) ,  B\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 5 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 4 operands: 5
3	Operation	operator: 6 operands: 7
4	Literal
5	ExprTuple	8, 22, 9
6	Literal
7	ExprTuple	10, 11, 12, 22
8	ExprRange	lambda_map: 13 start_index: 19 end_index: 16
9	ExprRange	lambda_map: 14 start_index: 19 end_index: 20
10	ExprRange	lambda_map: 15 start_index: 19 end_index: 16
11	Operation	operator: 25 operands: 17
12	ExprRange	lambda_map: 18 start_index: 19 end_index: 20
13	Lambda	parameter: 33 body: 27
14	Lambda	parameter: 33 body: 28
15	Lambda	parameter: 33 body: 21
16	Variable
17	ExprTuple	22, 29
18	Lambda	parameter: 33 body: 23
19	Literal
20	Variable
21	Operation	operator: 25 operands: 24
22	Variable
23	Operation	operator: 25 operands: 26
24	ExprTuple	27, 29
25	Literal
26	ExprTuple	28, 29
27	IndexedVar	variable: 30 index: 33
28	IndexedVar	variable: 31 index: 33
29	Literal
30	Variable
31	Variable
32	ExprTuple	33
33	Variable