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Expression of type Lambda

from the theory of proveit.numbers.multiplication

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, i, j
from proveit.core_expr_types import a_1_to_i, b_1_to_j
from proveit.logic import And, Equals, Forall, InSet
from proveit.numbers import Complex, Mult, Natural, zero
In [2]:
# build up the expression from sub-expressions
expr = Lambda([i, j], Conditional(Forall(instance_param_or_params = [a_1_to_i, b_1_to_j], instance_expr = Equals(Mult(a_1_to_i, zero, b_1_to_j), zero), domain = Complex), And(InSet(i, Natural), InSet(j, 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())
\left(i, j\right) \mapsto \left\{\forall_{a_{1}, a_{2}, \ldots, a_{i}, b_{1}, b_{2}, \ldots, b_{j} \in \mathbb{C}}~\left(\left(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{i} \cdot 0\cdot b_{1} \cdot  b_{2} \cdot  \ldots \cdot  b_{j}\right) = 0\right) \textrm{ if } i \in \mathbb{N} ,  j \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
0Lambdaparameters: 1
body: 2
1ExprTuple35, 38
2Conditionalvalue: 3
condition: 4
3Operationoperator: 5
operand: 8
4Operationoperator: 20
operands: 7
5Literal
6ExprTuple8
7ExprTuple9, 10
8Lambdaparameters: 11
body: 12
9Operationoperator: 40
operands: 13
10Operationoperator: 40
operands: 14
11ExprTuple29, 31
12Conditionalvalue: 15
condition: 16
13ExprTuple35, 17
14ExprTuple38, 17
15Operationoperator: 18
operands: 19
16Operationoperator: 20
operands: 21
17Literal
18Literal
19ExprTuple22, 30
20Literal
21ExprTuple23, 24
22Operationoperator: 25
operands: 26
23ExprRangelambda_map: 27
start_index: 37
end_index: 35
24ExprRangelambda_map: 28
start_index: 37
end_index: 38
25Literal
26ExprTuple29, 30, 31
27Lambdaparameter: 48
body: 32
28Lambdaparameter: 48
body: 33
29ExprRangelambda_map: 34
start_index: 37
end_index: 35
30Literal
31ExprRangelambda_map: 36
start_index: 37
end_index: 38
32Operationoperator: 40
operands: 39
33Operationoperator: 40
operands: 41
34Lambdaparameter: 48
body: 42
35Variable
36Lambdaparameter: 48
body: 43
37Literal
38Variable
39ExprTuple42, 44
40Literal
41ExprTuple43, 44
42IndexedVarvariable: 45
index: 48
43IndexedVarvariable: 46
index: 48
44Literal
45Variable
46Variable
47ExprTuple48
48Variable