Expression of type Lambda

from the theory of proveit.logic.booleans.conjunction

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 Conditional, Lambda, l, m, n
from proveit.core_expr_types import A_1_to_l, B_1_to_m, C_1_to_n
from proveit.logic import And, Forall, InSet
from proveit.numbers import Natural

# build up the expression from sub-expressions
sub_expr1 = [A_1_to_l, B_1_to_m, C_1_to_n]
expr = Lambda([l, m, n], Conditional(Forall(instance_param_or_params = sub_expr1, instance_expr = And(B_1_to_m), conditions = sub_expr1), 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_{1}, B_{2}, \ldots, B_{m}, C_{1}, C_{2}, \ldots, C_{n}~|~A_{1}, A_{2}, \ldots, A_{l},B_{1}, B_{2}, \ldots, B_{m},C_{1}, C_{2}, \ldots, C_{n}}~\left(B_{1} \land  B_{2} \land  \ldots \land  B_{m}\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	27, 29, 32
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 8
4	Operation	operator: 21 operands: 7
5	Literal
6	ExprTuple	8
7	ExprTuple	9, 10, 11
8	Lambda	parameters: 22 body: 12
9	Operation	operator: 15 operands: 13
10	Operation	operator: 15 operands: 14
11	Operation	operator: 15 operands: 16
12	Conditional	value: 17 condition: 18
13	ExprTuple	27, 19
14	ExprTuple	29, 19
15	Literal
16	ExprTuple	32, 19
17	Operation	operator: 21 operands: 20
18	Operation	operator: 21 operands: 22
19	Literal
20	ExprTuple	24
21	Literal
22	ExprTuple	23, 24, 25
23	ExprRange	lambda_map: 26 start_index: 31 end_index: 27
24	ExprRange	lambda_map: 28 start_index: 31 end_index: 29
25	ExprRange	lambda_map: 30 start_index: 31 end_index: 32
26	Lambda	parameter: 40 body: 33
27	Variable
28	Lambda	parameter: 40 body: 34
29	Variable
30	Lambda	parameter: 40 body: 35
31	Literal
32	Variable
33	IndexedVar	variable: 36 index: 40
34	IndexedVar	variable: 37 index: 40
35	IndexedVar	variable: 38 index: 40
36	Variable
37	Variable
38	Variable
39	ExprTuple	40
40	Variable