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, Conditional, ExprRange, IndexedVar, Lambda, Variable, m
from proveit.core_expr_types import A_1_to_m
from proveit.logic import FALSE, Forall, InSet, Not, Or
from proveit.numbers import Natural, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Lambda(m, Conditional(Forall(instance_param_or_params = [A_1_to_m], instance_expr = FALSE, conditions = [Or(A_1_to_m), ExprRange(sub_expr1, Not(IndexedVar(A, sub_expr1)), 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}~|~A_{1} \lor  A_{2} \lor  \ldots \lor  A_{m},(\lnot A_{1}), (\lnot A_{2}), \ldots, (\lnot A_{m})}~\bot \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: 25 body: 2
1	ExprTuple	25
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 9
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9
7	Literal
8	ExprTuple	25, 10
9	Lambda	parameters: 19 body: 11
10	Literal
11	Conditional	value: 12 condition: 13
12	Literal
13	Operation	operator: 14 operands: 15
14	Literal
15	ExprTuple	16, 17
16	Operation	operator: 18 operands: 19
17	ExprRange	lambda_map: 20 start_index: 24 end_index: 25
18	Literal
19	ExprTuple	21
20	Lambda	parameter: 31 body: 22
21	ExprRange	lambda_map: 23 start_index: 24 end_index: 25
22	Operation	operator: 26 operand: 28
23	Lambda	parameter: 31 body: 28
24	Literal
25	Variable
26	Literal
27	ExprTuple	28
28	IndexedVar	variable: 29 index: 31
29	Variable
30	ExprTuple	31
31	Variable