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 And, Not, Or
from proveit.numbers import one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Lambda([A_1_to_m], Conditional(Not(Or(A_1_to_m)), And(ExprRange(sub_expr1, Not(IndexedVar(A, sub_expr1)), one, m))))

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(A_{1}, A_{2}, \ldots, A_{m}\right) \mapsto \left\{\lnot \left(A_{1} \lor  A_{2} \lor  \ldots \lor  A_{m}\right) \textrm{ if } (\lnot A_{1}) \land  (\lnot A_{2}) \land  \ldots \land  (\lnot A_{m})\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 10 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 17 operand: 7
3	Operation	operator: 5 operands: 6
4	ExprTuple	7
5	Literal
6	ExprTuple	8
7	Operation	operator: 9 operands: 10
8	ExprRange	lambda_map: 11 start_index: 15 end_index: 16
9	Literal
10	ExprTuple	12
11	Lambda	parameter: 22 body: 13
12	ExprRange	lambda_map: 14 start_index: 15 end_index: 16
13	Operation	operator: 17 operand: 19
14	Lambda	parameter: 22 body: 19
15	Literal
16	Variable
17	Literal
18	ExprTuple	19
19	IndexedVar	variable: 20 index: 22
20	Variable
21	ExprTuple	22
22	Variable