Expression of type Lambda ¶

from the theory of proveit.logic.booleans.quantification.universality ¶

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, Q, R, m, n
from proveit.logic import And, Forall, Implies, InSet
from proveit.logic.booleans.quantification import general_bundled_forall_Pxy_if_Qx, general_nested_forall_Pxy_if_Qx
from proveit.numbers import NaturalPos

# build up the expression from sub-expressions
expr = Lambda([m, n], Conditional(Forall(instance_param_or_params = [P, Q, R], instance_expr = Implies(general_nested_forall_Pxy_if_Qx, general_bundled_forall_Pxy_if_Qx).with_wrapping_at(1)), And(InSet(m, NaturalPos), InSet(n, NaturalPos))))

# 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

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\left(m, n\right) \mapsto \left\{\forall_{P, Q, R}~\left(\begin{array}{c} \begin{array}{l} \left[\forall_{x_{1}, x_{2}, \ldots, x_{m}~|~Q\left(x_{1}, x_{2}, \ldots, x_{m}\right)}~\left[\forall_{y_{1}, y_{2}, \ldots, y_{n}~|~R\left(x_{1}, x_{2}, \ldots, x_{m},y_{1}, y_{2}, \ldots, y_{n}\right)}~P\left(x_{1}, x_{2}, \ldots, x_{m},y_{1}, y_{2}, \ldots, y_{n}\right)\right]\right] \\  \Rightarrow \left[\forall_{x_{1}, x_{2}, \ldots, x_{m}, y_{1}, y_{2}, \ldots, y_{n}~|~Q\left(x_{1}, x_{2}, \ldots, x_{m}\right), R\left(x_{1}, x_{2}, \ldots, x_{m},y_{1}, y_{2}, \ldots, y_{n}\right)}~P\left(x_{1}, x_{2}, \ldots, x_{m},y_{1}, y_{2}, \ldots, y_{n}\right)\right] \end{array} \end{array}\right) \textrm{ if } m \in \mathbb{N}^+ ,  n \in \mathbb{N}^+\right..

stored_expr.style_options()

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions
0	Lambda	parameters: 1 body: 2
1	ExprTuple	46, 49
2	Conditional	value: 3 condition: 4
3	Operation	operator: 28 operand: 7
4	Operation	operator: 30 operands: 6
5	ExprTuple	7
6	ExprTuple	8, 9
7	Lambda	parameters: 10 body: 11
8	Operation	operator: 13 operands: 12
9	Operation	operator: 13 operands: 14
10	ExprTuple	40, 36, 41
11	Operation	operator: 15 operands: 16
12	ExprTuple	46, 17
13	Literal
14	ExprTuple	49, 17
15	Literal
16	ExprTuple	18, 19
17	Literal
18	Operation	operator: 28 operand: 22
19	Operation	operator: 28 operand: 23
20	ExprTuple	22
21	ExprTuple	23
22	Lambda	parameters: 37 body: 24
23	Lambda	parameters: 42 body: 25
24	Conditional	value: 26 condition: 33
25	Conditional	value: 38 condition: 27
26	Operation	operator: 28 operand: 32
27	Operation	operator: 30 operands: 31
28	Literal
29	ExprTuple	32
30	Literal
31	ExprTuple	33, 39
32	Lambda	parameters: 34 body: 35
33	Operation	operator: 36 operands: 37
34	ExprTuple	44
35	Conditional	value: 38 condition: 39
36	Variable
37	ExprTuple	43
38	Operation	operator: 40 operands: 42
39	Operation	operator: 41 operands: 42
40	Variable
41	Variable
42	ExprTuple	43, 44
43	ExprRange	lambda_map: 45 start_index: 48 end_index: 46
44	ExprRange	lambda_map: 47 start_index: 48 end_index: 49
45	Lambda	parameter: 55 body: 50
46	Variable
47	Lambda	parameter: 55 body: 51
48	Literal
49	Variable
50	IndexedVar	variable: 52 index: 55
51	IndexedVar	variable: 53 index: 55
52	Variable
53	Variable
54	ExprTuple	55
55	Variable

Expression of type Lambda¶

from the theory of proveit.logic.booleans.quantification.universality¶

Expression of type Lambda ¶

from the theory of proveit.logic.booleans.quantification.universality ¶