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 B, Conditional, Lambda, l, m, n
from proveit.core_expr_types import A_1_to_l, C_1_to_m, D_1_to_n
from proveit.logic import And, Forall, InSet, Or
from proveit.numbers import Natural

# build up the expression from sub-expressions
expr = Lambda([l, m, n], Conditional(Forall(instance_param_or_params = [A_1_to_l, B, C_1_to_m, D_1_to_n], instance_expr = Or(A_1_to_l, C_1_to_m, B, D_1_to_n), condition = Or(A_1_to_l, B, C_1_to_m, D_1_to_n)), And(InSet(l, Natural), InSet(m, Natural), InSet(n, Natural))))

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