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, m, n
from proveit.core_expr_types import A_1_to_m, C_1_to_n
from proveit.logic import And, Boolean, Forall, InSet, Or
from proveit.numbers import Natural

# build up the expression from sub-expressions
expr = Lambda([m, n], Conditional(Forall(instance_param_or_params = [A_1_to_m, B, C_1_to_n], instance_expr = Or(A_1_to_m, B, C_1_to_n), domain = Boolean, condition = B), And(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(m, n\right) \mapsto \left\{\forall_{A_{1}, A_{2}, \ldots, A_{m}, B, C_{1}, C_{2}, \ldots, C_{n} \in \mathbb{B}~|~B}~\left(A_{1} \lor  A_{2} \lor  \ldots \lor  A_{m} \lor B\lor C_{1} \lor  C_{2} \lor  \ldots \lor  C_{n}\right) \textrm{ if } 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, 33
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 8
4	Operation	operator: 19 operands: 7
5	Literal
6	ExprTuple	8
7	ExprTuple	9, 10
8	Lambda	parameters: 18 body: 11
9	Operation	operator: 38 operands: 12
10	Operation	operator: 38 operands: 13
11	Conditional	value: 14 condition: 15
12	ExprTuple	29, 16
13	ExprTuple	33, 16
14	Operation	operator: 17 operands: 18
15	Operation	operator: 19 operands: 20
16	Literal
17	Literal
18	ExprTuple	21, 35, 22
19	Literal
20	ExprTuple	23, 24, 25, 35
21	ExprRange	lambda_map: 26 start_index: 32 end_index: 29
22	ExprRange	lambda_map: 27 start_index: 32 end_index: 33
23	ExprRange	lambda_map: 28 start_index: 32 end_index: 29
24	Operation	operator: 38 operands: 30
25	ExprRange	lambda_map: 31 start_index: 32 end_index: 33
26	Lambda	parameter: 46 body: 40
27	Lambda	parameter: 46 body: 41
28	Lambda	parameter: 46 body: 34
29	Variable
30	ExprTuple	35, 42
31	Lambda	parameter: 46 body: 36
32	Literal
33	Variable
34	Operation	operator: 38 operands: 37
35	Variable
36	Operation	operator: 38 operands: 39
37	ExprTuple	40, 42
38	Literal
39	ExprTuple	41, 42
40	IndexedVar	variable: 43 index: 46
41	IndexedVar	variable: 44 index: 46
42	Literal
43	Variable
44	Variable
45	ExprTuple	46
46	Variable