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.core_expr_types import A_1_to_m
from proveit.logic import And, Boolean, Forall, InSet, Or
from proveit.numbers import Add, NaturalPos, 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(m, Conditional(Forall(instance_param_or_params = [ExprRange(sub_expr1, sub_expr2, one, Add(m, two))], instance_expr = InSet(Or(ExprRange(sub_expr1, sub_expr2, one, sub_expr3)), Boolean), condition = ExprRange(sub_expr1, InSet(sub_expr2, Boolean), one, sub_expr3)), And(InSet(m, NaturalPos), Forall(instance_param_or_params = [A_1_to_m], instance_expr = InSet(Or(A_1_to_m), Boolean), domain = Boolean))))

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())

m \mapsto \left\{\forall_{A_{1}, A_{2}, \ldots, A_{m + 2}~|~\left(A_{1} \in \mathbb{B}\right), \left(A_{2} \in \mathbb{B}\right), \ldots, \left(A_{m + 1} \in \mathbb{B}\right)}~\left(\left(A_{1} \lor  A_{2} \lor  \ldots \lor  A_{m + 1}\right) \in \mathbb{B}\right) \textrm{ if } m \in \mathbb{N}^+ ,  \forall_{A_{1}, A_{2}, \ldots, A_{m} \in \mathbb{B}}~\left(\left(A_{1} \lor  A_{2} \lor  \ldots \lor  A_{m}\right) \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	parameter: 47 body: 2
1	ExprTuple	47
2	Conditional	value: 3 condition: 4
3	Operation	operator: 13 operand: 7
4	Operation	operator: 32 operands: 6
5	ExprTuple	7
6	ExprTuple	8, 9
7	Lambda	parameters: 10 body: 11
8	Operation	operator: 48 operands: 12
9	Operation	operator: 13 operand: 19
10	ExprTuple	15
11	Conditional	value: 16 condition: 17
12	ExprTuple	47, 18
13	Literal
14	ExprTuple	19
15	ExprRange	lambda_map: 45 start_index: 46 end_index: 20
16	Operation	operator: 48 operands: 21
17	Operation	operator: 32 operands: 22
18	Literal
19	Lambda	parameters: 39 body: 23
20	Operation	operator: 41 operands: 24
21	ExprTuple	25, 51
22	ExprTuple	26
23	Conditional	value: 27 condition: 28
24	ExprTuple	47, 29
25	Operation	operator: 38 operands: 30
26	ExprRange	lambda_map: 40 start_index: 46 end_index: 37
27	Operation	operator: 48 operands: 31
28	Operation	operator: 32 operands: 33
29	Literal
30	ExprTuple	34
31	ExprTuple	35, 51
32	Literal
33	ExprTuple	36
34	ExprRange	lambda_map: 45 start_index: 46 end_index: 37
35	Operation	operator: 38 operands: 39
36	ExprRange	lambda_map: 40 start_index: 46 end_index: 47
37	Operation	operator: 41 operands: 42
38	Literal
39	ExprTuple	43
40	Lambda	parameter: 54 body: 44
41	Literal
42	ExprTuple	47, 46
43	ExprRange	lambda_map: 45 start_index: 46 end_index: 47
44	Operation	operator: 48 operands: 49
45	Lambda	parameter: 54 body: 50
46	Literal
47	Variable
48	Literal
49	ExprTuple	50, 51
50	IndexedVar	variable: 52 index: 54
51	Literal
52	Variable
53	ExprTuple	54
54	Variable