Expression of type Lambda

from the theory of proveit.core_expr_types.conditionals

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, a, m, n
from proveit.core_expr_types import Q_1_to_m, R_1_to_n
from proveit.logic import And, Equals, Forall, InSet
from proveit.numbers import Natural

# build up the expression from sub-expressions
expr = Lambda([m, n], Conditional(Forall(instance_param_or_params = [a, Q_1_to_m, R_1_to_n], instance_expr = Equals(Conditional(a, And(And(Q_1_to_m), And(R_1_to_n))), Conditional(a, And(Q_1_to_m, R_1_to_n))).with_wrapping_at(1)), And(InSet(m, Natural), InSet(n, Natural))))

expr:

# 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_{a, Q_{1}, Q_{2}, \ldots, Q_{m}, R_{1}, R_{2}, \ldots, R_{n}}~\left(\begin{array}{c} \begin{array}{l} \left\{a \textrm{ if } Q_{1} \land  Q_{2} \land  \ldots \land  Q_{m} ,  R_{1} \land  R_{2} \land  \ldots \land  R_{n}\right.. \\  = \left\{a \textrm{ if } Q_{1} ,  Q_{2} ,  \ldots ,  Q_{m}, R_{1} ,  R_{2} ,  \ldots ,  R_{n}\right.. \end{array} \end{array}\right) \textrm{ if } m \in \mathbb{N} ,  n \in \mathbb{N}\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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