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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, m
from proveit.core_expr_types import A_1_to_m
from proveit.logic import And, Boolean, Forall, InSet
from proveit.numbers import Natural
In [2]:
# build up the expression from sub-expressions
expr = Lambda(m, Conditional(Forall(instance_param_or_params = [A_1_to_m], instance_expr = InSet(And(A_1_to_m), Boolean), domain = Boolean), InSet(m, Natural)))
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())
m \mapsto \left\{\forall_{A_{1}, A_{2}, \ldots, A_{m} \in \mathbb{B}}~\left(\left(A_{1} \land  A_{2} \land  \ldots \land  A_{m}\right) \in \mathbb{B}\right) \textrm{ if } m \in \mathbb{N}\right..
In [5]:
stored_expr.style_options()
no style options
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Lambdaparameter: 24
body: 2
1ExprTuple24
2Conditionalvalue: 3
condition: 4
3Operationoperator: 5
operand: 8
4Operationoperator: 25
operands: 7
5Literal
6ExprTuple8
7ExprTuple24, 9
8Lambdaparameters: 18
body: 10
9Literal
10Conditionalvalue: 11
condition: 12
11Operationoperator: 25
operands: 13
12Operationoperator: 17
operands: 14
13ExprTuple15, 28
14ExprTuple16
15Operationoperator: 17
operands: 18
16ExprRangelambda_map: 19
start_index: 23
end_index: 24
17Literal
18ExprTuple20
19Lambdaparameter: 31
body: 21
20ExprRangelambda_map: 22
start_index: 23
end_index: 24
21Operationoperator: 25
operands: 26
22Lambdaparameter: 31
body: 27
23Literal
24Variable
25Literal
26ExprTuple27, 28
27IndexedVarvariable: 29
index: 31
28Literal
29Variable
30ExprTuple31
31Variable