logo

Expression of type Lambda

from the theory of proveit.logic.booleans.conjunction

In [1]:
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 Conditional, Lambda
from proveit.core_expr_types import A_1_to_l, B_1_to_m, C_1_to_n
from proveit.logic import And
In [2]:
# build up the expression from sub-expressions
expr = Lambda([A_1_to_l, B_1_to_m, C_1_to_n], Conditional(And(A_1_to_l, B_1_to_m, C_1_to_n), And(A_1_to_l, And(B_1_to_m), C_1_to_n)))
expr:
In [3]:
# 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
In [4]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())
\left(A_{1}, A_{2}, \ldots, A_{l}, B_{1}, B_{2}, \ldots, B_{m}, C_{1}, C_{2}, \ldots, C_{n}\right) \mapsto \left\{A_{1} \land  A_{2} \land  \ldots \land  A_{l}\land B_{1} \land  B_{2} \land  \ldots \land  B_{m}\land C_{1} \land  C_{2} \land  \ldots \land  C_{n} \textrm{ if } A_{1} ,  A_{2} ,  \ldots ,  A_{l} ,  B_{1} \land  B_{2} \land  \ldots \land  B_{m}, C_{1} ,  C_{2} ,  \ldots ,  C_{n}\right..
In [5]:
stored_expr.style_options()
no style options
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Lambdaparameters: 4
body: 1
1Conditionalvalue: 2
condition: 3
2Operationoperator: 11
operands: 4
3Operationoperator: 11
operands: 5
4ExprTuple6, 16, 8
5ExprTuple6, 7, 8
6ExprRangelambda_map: 9
start_index: 20
end_index: 10
7Operationoperator: 11
operands: 12
8ExprRangelambda_map: 13
start_index: 20
end_index: 14
9Lambdaparameter: 26
body: 15
10Variable
11Literal
12ExprTuple16
13Lambdaparameter: 26
body: 17
14Variable
15IndexedVarvariable: 18
index: 26
16ExprRangelambda_map: 19
start_index: 20
end_index: 21
17IndexedVarvariable: 22
index: 26
18Variable
19Lambdaparameter: 26
body: 23
20Literal
21Variable
22Variable
23IndexedVarvariable: 24
index: 26
24Variable
25ExprTuple26
26Variable