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
expr = Lambda([l, m, n], Conditional(Forall(instance_param_or_params = [A_1_to_l, B_1_to_m, C_1_to_n], instance_expr = And(A_1_to_l, B_1_to_m, C_1_to_n), condition = And(A_1_to_l, And(B_1_to_m), C_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_{1}, B_{2}, \ldots, B_{m}, C_{1}, C_{2}, \ldots, C_{n}~|~A_{1}, A_{2}, \ldots, A_{l}, B_{1} \land  B_{2} \land  \ldots \land  B_{m},C_{1}, C_{2}, \ldots, C_{n}}~\left(A_{1} \land  A_{2} \land  \ldots \land  A_{l}\land B_{1} \land  B_{2} \land  \ldots \land  B_{m}\land C_{1} \land  C_{2} \land  \ldots \land  C_{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	26, 37, 30
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 8
4	Operation	operator: 27 operands: 7
5	Literal
6	ExprTuple	8
7	ExprTuple	9, 10, 11
8	Lambda	parameters: 20 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	26, 19
14	ExprTuple	37, 19
15	Literal
16	ExprTuple	30, 19
17	Operation	operator: 27 operands: 20
18	Operation	operator: 27 operands: 21
19	Literal
20	ExprTuple	22, 32, 24
21	ExprTuple	22, 23, 24
22	ExprRange	lambda_map: 25 start_index: 36 end_index: 26
23	Operation	operator: 27 operands: 28
24	ExprRange	lambda_map: 29 start_index: 36 end_index: 30
25	Lambda	parameter: 42 body: 31
26	Variable
27	Literal
28	ExprTuple	32
29	Lambda	parameter: 42 body: 33
30	Variable
31	IndexedVar	variable: 34 index: 42
32	ExprRange	lambda_map: 35 start_index: 36 end_index: 37
33	IndexedVar	variable: 38 index: 42
34	Variable
35	Lambda	parameter: 42 body: 39
36	Literal
37	Variable
38	Variable
39	IndexedVar	variable: 40 index: 42
40	Variable
41	ExprTuple	42
42	Variable