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 C, Conditional, Lambda, l, m, n
from proveit.core_expr_types import A_1_to_l, B_1_to_m, D_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, D_1_to_n], instance_expr = And(A_1_to_l, C, B_1_to_m, D_1_to_n), condition = And(A_1_to_l, B_1_to_m, C, 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_{1}, B_{2}, \ldots, B_{m}, C, D_{1}, D_{2}, \ldots, D_{n}~|~A_{1}, A_{2}, \ldots, A_{l},B_{1}, B_{2}, \ldots, B_{m}, C,D_{1}, D_{2}, \ldots, D_{n}}~\left(A_{1} \land  A_{2} \land  \ldots \land  A_{l} \land C\land B_{1} \land  B_{2} \land  \ldots \land  B_{m}\land D_{1} \land  D_{2} \land  \ldots \land  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	28, 30, 33
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	28, 19
14	ExprTuple	30, 19
15	Literal
16	ExprTuple	33, 19
17	Operation	operator: 21 operands: 20
18	Operation	operator: 21 operands: 22
19	Literal
20	ExprTuple	23, 25, 24, 26
21	Literal
22	ExprTuple	23, 24, 25, 26
23	ExprRange	lambda_map: 27 start_index: 32 end_index: 28
24	ExprRange	lambda_map: 29 start_index: 32 end_index: 30
25	Variable
26	ExprRange	lambda_map: 31 start_index: 32 end_index: 33
27	Lambda	parameter: 41 body: 34
28	Variable
29	Lambda	parameter: 41 body: 35
30	Variable
31	Lambda	parameter: 41 body: 36
32	Literal
33	Variable
34	IndexedVar	variable: 37 index: 41
35	IndexedVar	variable: 38 index: 41
36	IndexedVar	variable: 39 index: 41
37	Variable
38	Variable
39	Variable
40	ExprTuple	41
41	Variable