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Expression of type Lambda

from the theory of proveit.logic.equality

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, P, n
from proveit.core_expr_types import P__x_1_to_n, P__y_1_to_n, x_1_to_n, y_1_to_n
from proveit.logic import Equals, Forall, InSet
from proveit.numbers import Natural
In [2]:
# build up the expression from sub-expressions
expr = Lambda(n, Conditional(Forall(instance_param_or_params = [P, x_1_to_n, y_1_to_n], instance_expr = P__x_1_to_n, conditions = [P__y_1_to_n, Equals([x_1_to_n], [y_1_to_n])]), InSet(n, 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())
n \mapsto \left\{\forall_{P, x_{1}, x_{2}, \ldots, x_{n}, y_{1}, y_{2}, \ldots, y_{n}~|~P\left(y_{1}, y_{2}, \ldots, y_{n}\right), \left(x_{1}, x_{2}, \ldots, x_{n}\right) = \left(y_{1}, y_{2}, \ldots, y_{n}\right)}~P\left(x_{1}, x_{2}, \ldots, x_{n}\right) \textrm{ if } n \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: 29
body: 2
1ExprTuple29
2Conditionalvalue: 3
condition: 4
3Operationoperator: 5
operand: 9
4Operationoperator: 7
operands: 8
5Literal
6ExprTuple9
7Literal
8ExprTuple29, 10
9Lambdaparameters: 11
body: 12
10Literal
11ExprTuple19, 24, 25
12Conditionalvalue: 13
condition: 14
13Operationoperator: 19
operands: 22
14Operationoperator: 15
operands: 16
15Literal
16ExprTuple17, 18
17Operationoperator: 19
operands: 23
18Operationoperator: 20
operands: 21
19Variable
20Literal
21ExprTuple22, 23
22ExprTuple24
23ExprTuple25
24ExprRangelambda_map: 26
start_index: 28
end_index: 29
25ExprRangelambda_map: 27
start_index: 28
end_index: 29
26Lambdaparameter: 35
body: 30
27Lambdaparameter: 35
body: 31
28Literal
29Variable
30IndexedVarvariable: 32
index: 35
31IndexedVarvariable: 33
index: 35
32Variable
33Variable
34ExprTuple35
35Variable