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 B, Conditional, Lambda, m, n
from proveit.core_expr_types import A_1_to_m, C_1_to_n
from proveit.logic import And, Forall, InSet, Not
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 = Not(And(A_1_to_m, B, C_1_to_n)), condition = Not(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}~|~\lnot B}~(\lnot \left(A_{1} \land  A_{2} \land  \ldots \land  A_{m} \land B\land C_{1} \land  C_{2} \land  \ldots \land  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	28, 31
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 8
4	Operation	operator: 22 operands: 7
5	Literal
6	ExprTuple	8
7	ExprTuple	9, 10
8	Lambda	parameters: 23 body: 11
9	Operation	operator: 13 operands: 12
10	Operation	operator: 13 operands: 14
11	Conditional	value: 15 condition: 16
12	ExprTuple	28, 17
13	Literal
14	ExprTuple	31, 17
15	Operation	operator: 19 operand: 21
16	Operation	operator: 19 operand: 25
17	Literal
18	ExprTuple	21
19	Literal
20	ExprTuple	25
21	Operation	operator: 22 operands: 23
22	Literal
23	ExprTuple	24, 25, 26
24	ExprRange	lambda_map: 27 start_index: 30 end_index: 28
25	Variable
26	ExprRange	lambda_map: 29 start_index: 30 end_index: 31
27	Lambda	parameter: 37 body: 32
28	Variable
29	Lambda	parameter: 37 body: 33
30	Literal
31	Variable
32	IndexedVar	variable: 34 index: 37
33	IndexedVar	variable: 35 index: 37
34	Variable
35	Variable
36	ExprTuple	37
37	Variable