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 A, C, Conditional, ExprRange, IndexedVar, Lambda, Variable, m, n
from proveit.core_expr_types import A_1_to_m, C_1_to_n
from proveit.logic import And, Boolean, Equals, FALSE, InSet
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, C_1_to_n], Conditional(Equals(And(A_1_to_m, FALSE, C_1_to_n), FALSE), And(ExprRange(sub_expr1, InSet(IndexedVar(A, sub_expr1), Boolean), one, m), ExprRange(sub_expr1, InSet(IndexedVar(C, sub_expr1), Boolean), one, n))))

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}, C_{1}, C_{2}, \ldots, C_{n}\right) \mapsto \left\{\left(A_{1} \land  A_{2} \land  \ldots \land  A_{m} \land \bot\land C_{1} \land  C_{2} \land  \ldots \land  C_{n}\right) = \bot \textrm{ if } \left(A_{1} \in \mathbb{B}\right) ,  \left(A_{2} \in \mathbb{B}\right) ,  \ldots ,  \left(A_{m} \in \mathbb{B}\right), \left(C_{1} \in \mathbb{B}\right) ,  \left(C_{2} \in \mathbb{B}\right) ,  \ldots ,  \left(C_{n} \in \mathbb{B}\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: 1 body: 2
1	ExprTuple	15, 17
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 11 operands: 7
5	Literal
6	ExprTuple	8, 16
7	ExprTuple	9, 10
8	Operation	operator: 11 operands: 12
9	ExprRange	lambda_map: 13 start_index: 23 end_index: 21
10	ExprRange	lambda_map: 14 start_index: 23 end_index: 24
11	Literal
12	ExprTuple	15, 16, 17
13	Lambda	parameter: 34 body: 18
14	Lambda	parameter: 34 body: 19
15	ExprRange	lambda_map: 20 start_index: 23 end_index: 21
16	Literal
17	ExprRange	lambda_map: 22 start_index: 23 end_index: 24
18	Operation	operator: 26 operands: 25
19	Operation	operator: 26 operands: 27
20	Lambda	parameter: 34 body: 28
21	Variable
22	Lambda	parameter: 34 body: 29
23	Literal
24	Variable
25	ExprTuple	28, 30
26	Literal
27	ExprTuple	29, 30
28	IndexedVar	variable: 31 index: 34
29	IndexedVar	variable: 32 index: 34
30	Literal
31	Variable
32	Variable
33	ExprTuple	34
34	Variable