Proof: Begin Constructor Arguments Property Example

Let's prove the following theorem:

if the following are true:

expression state at time 9 = "begin_expr"
the expression at time 9 = Person("John", "Smith", 25)
arguments stack at time 9 = [ ]

then arguments stack at time 10 = [ [ "John", [ "Smith", [ 25, [ ] ] ] ], [ ] ]

Code Editor

LW Python State

Current Line

Current Tab

Time

LW Python Simulator

Proof:

View as a tree | View dependent proofs | Try proving it

Given

1	expression state at time 9 = "begin_expr"
2	the expression at time 9 = `Person("John", "Smith", 25)`
3	arguments stack at time 9 = [ ]

Proof Table

#	Claim	Reason
1	arguments stack at time (9 + 1) = [ [ "John", [ "Smith", [ 25, [ ] ] ] ], arguments stack at time 9 ]	if expression state at time 9 = "begin_expr" and the expression at time 9 = `Person("John", "Smith", 25)`, then arguments stack at time (9 + 1) = [ [ "John", [ "Smith", [ 25, [ ] ] ] ], arguments stack at time 9 ] (Begin Constructor Arguments Property)
2	[ [ "John", [ "Smith", [ 25, [ ] ] ] ], arguments stack at time 9 ] = [ [ "John", [ "Smith", [ 25, [ ] ] ] ], [ ] ]	if arguments stack at time 9 = [ ], then [ [ "John", [ "Smith", [ 25, [ ] ] ] ], arguments stack at time 9 ] = [ [ "John", [ "Smith", [ 25, [ ] ] ] ], [ ] ] (Substitution)
3	arguments stack at time (9 + 1) = [ [ "John", [ "Smith", [ 25, [ ] ] ] ], [ ] ]	if arguments stack at time (9 + 1) = [ [ "John", [ "Smith", [ 25, [ ] ] ] ], arguments stack at time 9 ] and [ [ "John", [ "Smith", [ 25, [ ] ] ] ], arguments stack at time 9 ] = [ [ "John", [ "Smith", [ 25, [ ] ] ] ], [ ] ], then arguments stack at time (9 + 1) = [ [ "John", [ "Smith", [ 25, [ ] ] ] ], [ ] ] (Transitive Property of Equality)
4	9 + 1 = 10	9 + 1 = 10 (Fixed Value Statement)
5	arguments stack at time (9 + 1) = arguments stack at time 10	if 9 + 1 = 10, then arguments stack at time (9 + 1) = arguments stack at time 10 (Substitution)
6	arguments stack at time 10 = [ [ "John", [ "Smith", [ 25, [ ] ] ] ], [ ] ]	if arguments stack at time (9 + 1) = arguments stack at time 10 and arguments stack at time (9 + 1) = [ [ "John", [ "Smith", [ 25, [ ] ] ] ], [ ] ], then arguments stack at time 10 = [ [ "John", [ "Smith", [ 25, [ ] ] ] ], [ ] ] (Transitive Property of Equality Variation 2)

Comments

Please log in to add comments