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 A, B, Conditional, ExprRange, IndexedVar, Lambda, Variable, m
from proveit.core_expr_types import A_1_to_m, B_1_to_m
from proveit.logic import Boolean, Forall, Implies, InSet, Not, Or
from proveit.numbers import Natural, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = IndexedVar(B, sub_expr1)
sub_expr3 = IndexedVar(A, sub_expr1)
expr = Lambda(m, Conditional(Forall(instance_param_or_params = [A_1_to_m, B_1_to_m], instance_expr = Or(ExprRange(sub_expr1, Not(sub_expr2), one, m)), domain = Boolean, conditions = [Or(ExprRange(sub_expr1, Not(sub_expr3), one, m)), ExprRange(sub_expr1, Implies(sub_expr3, sub_expr2), one, m)]), InSet(m, 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())

m \mapsto \left\{\forall_{A_{1}, A_{2}, \ldots, A_{m}, B_{1}, B_{2}, \ldots, B_{m} \in \mathbb{B}~|~(\lnot A_{1}) \lor  (\lnot A_{2}) \lor  \ldots \lor  (\lnot A_{m}),\left(A_{1} \Rightarrow B_{1}\right), \left(A_{2} \Rightarrow B_{2}\right), \ldots, \left(A_{m} \Rightarrow B_{m}\right)}~\left((\lnot B_{1}) \lor  (\lnot B_{2}) \lor  \ldots \lor  (\lnot B_{m})\right) \textrm{ if } m \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	parameter: 43 body: 2
1	ExprTuple	43
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 8
4	Operation	operator: 39 operands: 7
5	Literal
6	ExprTuple	8
7	ExprTuple	43, 9
8	Lambda	parameters: 10 body: 11
9	Literal
10	ExprTuple	12, 13
11	Conditional	value: 14 condition: 15
12	ExprRange	lambda_map: 16 start_index: 42 end_index: 43
13	ExprRange	lambda_map: 17 start_index: 42 end_index: 43
14	Operation	operator: 29 operands: 18
15	Operation	operator: 19 operands: 20
16	Lambda	parameter: 55 body: 52
17	Lambda	parameter: 55 body: 48
18	ExprTuple	21
19	Literal
20	ExprTuple	22, 23, 24, 25
21	ExprRange	lambda_map: 26 start_index: 42 end_index: 43
22	ExprRange	lambda_map: 27 start_index: 42 end_index: 43
23	ExprRange	lambda_map: 28 start_index: 42 end_index: 43
24	Operation	operator: 29 operands: 30
25	ExprRange	lambda_map: 31 start_index: 42 end_index: 43
26	Lambda	parameter: 55 body: 32
27	Lambda	parameter: 55 body: 33
28	Lambda	parameter: 55 body: 34
29	Literal
30	ExprTuple	35
31	Lambda	parameter: 55 body: 36
32	Operation	operator: 49 operand: 48
33	Operation	operator: 39 operands: 38
34	Operation	operator: 39 operands: 40
35	ExprRange	lambda_map: 41 start_index: 42 end_index: 43
36	Operation	operator: 44 operands: 45
37	ExprTuple	48
38	ExprTuple	52, 46
39	Literal
40	ExprTuple	48, 46
41	Lambda	parameter: 55 body: 47
42	Literal
43	Variable
44	Literal
45	ExprTuple	52, 48
46	Literal
47	Operation	operator: 49 operand: 52
48	IndexedVar	variable: 51 index: 55
49	Literal
50	ExprTuple	52
51	Variable
52	IndexedVar	variable: 53 index: 55
53	Variable
54	ExprTuple	55
55	Variable