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Expression of type Lambda

from the theory of proveit.numbers.numerals.decimals

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, Function, Lambda, f, i, j
from proveit.core_expr_types import f_i_to_j
from proveit.logic import Equals
from proveit.numbers import Add, one, two
In [2]:
# build up the expression from sub-expressions
sub_expr1 = Add(i, two)
expr = Lambda([f, i, j], Conditional(Equals([f_i_to_j], [Function(f, [i]), Function(f, [Add(i, one)]), Function(f, [sub_expr1])]), Equals(j, sub_expr1)))
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, i, j\right) \mapsto \left\{\left(f\left(i\right), f\left(i + 1\right), \ldots, f\left(j\right)\right) = \left(f\left(i\right), f\left(i + 1\right), f\left(i + 2\right)\right) \textrm{ if } j = \left(i + 2\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
1ExprTuple22, 29, 15
2Conditionalvalue: 3
condition: 4
3Operationoperator: 6
operands: 5
4Operationoperator: 6
operands: 7
5ExprTuple8, 9
6Literal
7ExprTuple15, 21
8ExprTuple10
9ExprTuple11, 12, 13
10ExprRangelambda_map: 14
start_index: 29
end_index: 15
11Operationoperator: 22
operand: 29
12Operationoperator: 22
operand: 20
13Operationoperator: 22
operand: 21
14Lambdaparameter: 27
body: 19
15Variable
16ExprTuple29
17ExprTuple20
18ExprTuple21
19Operationoperator: 22
operand: 27
20Operationoperator: 25
operands: 24
21Operationoperator: 25
operands: 26
22Variable
23ExprTuple27
24ExprTuple29, 28
25Literal
26ExprTuple29, 30
27Variable
28Literal
29Variable
30Literal