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, Conditional, ExprRange, IndexedVar, Lambda, Variable, m
from proveit.logic import And, Boolean, InSet, Or
from proveit.numbers import Add, one, two

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = IndexedVar(A, sub_expr1)
sub_expr3 = Add(m, one)
expr = Lambda([ExprRange(sub_expr1, sub_expr2, one, Add(m, two))], Conditional(InSet(Or(ExprRange(sub_expr1, sub_expr2, one, sub_expr3)), Boolean), And(ExprRange(sub_expr1, InSet(sub_expr2, Boolean), one, sub_expr3))))

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 + 2}\right) \mapsto \left\{\left(A_{1} \lor  A_{2} \lor  \ldots \lor  A_{m + 1}\right) \in \mathbb{B} \textrm{ if } \left(A_{1} \in \mathbb{B}\right) \land  \left(A_{2} \in \mathbb{B}\right) \land  \ldots \land  \left(A_{m + 1} \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: 1 body: 2
1	ExprTuple	3
2	Conditional	value: 4 condition: 5
3	ExprRange	lambda_map: 19 start_index: 28 end_index: 6
4	Operation	operator: 21 operands: 7
5	Operation	operator: 8 operands: 9
6	Operation	operator: 23 operands: 10
7	ExprTuple	11, 26
8	Literal
9	ExprTuple	12
10	ExprTuple	27, 13
11	Operation	operator: 14 operands: 15
12	ExprRange	lambda_map: 16 start_index: 28 end_index: 20
13	Literal
14	Literal
15	ExprTuple	17
16	Lambda	parameter: 31 body: 18
17	ExprRange	lambda_map: 19 start_index: 28 end_index: 20
18	Operation	operator: 21 operands: 22
19	Lambda	parameter: 31 body: 25
20	Operation	operator: 23 operands: 24
21	Literal
22	ExprTuple	25, 26
23	Literal
24	ExprTuple	27, 28
25	IndexedVar	variable: 29 index: 31
26	Literal
27	Variable
28	Literal
29	Variable
30	ExprTuple	31
31	Variable