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, Equals, FALSE, InSet, Or, Set
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(Equals(Or(A_1_to_m), FALSE), And(ExprRange(sub_expr1, InSet(IndexedVar(A, sub_expr1), Set(FALSE)), 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\{\left(A_{1} \lor  A_{2} \lor  \ldots \lor  A_{m}\right) = \bot \textrm{ if } \left(A_{1} \in \left\{\bot\right\}\right) \land  \left(A_{2} \in \left\{\bot\right\}\right) \land  \ldots \land  \left(A_{m} \in \left\{\bot\right\}\right)\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 11 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 4 operands: 5
3	Operation	operator: 6 operands: 7
4	Literal
5	ExprTuple	8, 27
6	Literal
7	ExprTuple	9
8	Operation	operator: 10 operands: 11
9	ExprRange	lambda_map: 12 start_index: 16 end_index: 17
10	Literal
11	ExprTuple	13
12	Lambda	parameter: 26 body: 14
13	ExprRange	lambda_map: 15 start_index: 16 end_index: 17
14	Operation	operator: 18 operands: 19
15	Lambda	parameter: 26 body: 20
16	Literal
17	Variable
18	Literal
19	ExprTuple	20, 21
20	IndexedVar	variable: 22 index: 26
21	Operation	operator: 24 operand: 27
22	Variable
23	ExprTuple	26
24	Literal
25	ExprTuple	27
26	Variable
27	Literal