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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, f
from proveit.core_expr_types import f__x_1_to_n, f__y_1_to_n, x_1_to_n, x_eq_y__1_to_n, y_1_to_n
from proveit.logic import And, Equals
In [2]:
# build up the expression from sub-expressions
expr = Lambda([f, x_1_to_n, y_1_to_n], Conditional(Equals(f__x_1_to_n, f__y_1_to_n), And(x_eq_y__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(f, x_{1}, x_{2}, \ldots, x_{n}, y_{1}, y_{2}, \ldots, y_{n}\right) \mapsto \left\{f\left(x_{1}, x_{2}, \ldots, x_{n}\right) = f\left(y_{1}, y_{2}, \ldots, y_{n}\right) \textrm{ if } \left(x_{1} = y_{1}\right) \land  \left(x_{2} = y_{2}\right) \land  \ldots \land  \left(x_{n} = y_{n}\right)\right..
In [5]:
stored_expr.style_options()
no style options
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Lambdaparameters: 1
body: 2
1ExprTuple12, 15, 16
2Conditionalvalue: 3
condition: 4
3Operationoperator: 22
operands: 5
4Operationoperator: 6
operands: 7
5ExprTuple8, 9
6Literal
7ExprTuple10
8Operationoperator: 12
operands: 11
9Operationoperator: 12
operands: 13
10ExprRangelambda_map: 14
start_index: 20
end_index: 21
11ExprTuple15
12Variable
13ExprTuple16
14Lambdaparameter: 29
body: 17
15ExprRangelambda_map: 18
start_index: 20
end_index: 21
16ExprRangelambda_map: 19
start_index: 20
end_index: 21
17Operationoperator: 22
operands: 23
18Lambdaparameter: 29
body: 24
19Lambdaparameter: 29
body: 25
20Literal
21Variable
22Literal
23ExprTuple24, 25
24IndexedVarvariable: 26
index: 29
25IndexedVarvariable: 27
index: 29
26Variable
27Variable
28ExprTuple29
29Variable