Proof: Get Begin Expr Parent 3

Let's prove the following theorem:

if the following are true:

expression state at time 3 = "begin_expr"
the expression at time 3 = entry "ES": "Estonia"
parent stack at time 3 = [ {"ES": "Estonia", "MX": "Mexico"}, [ ] ]

then parent stack at time 4 = [ entry "ES": "Estonia", [ {"ES": "Estonia", "MX": "Mexico"}, [ ] ] ]

Proof:

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

Given

1	expression state at time 3 = "begin_expr"
2	the expression at time 3 = entry "ES": "Estonia"
3	parent stack at time 3 = [ `{"ES": "Estonia", "MX": "Mexico"}`, [ ] ]

Proof Table

#	Claim	Reason
1	parent stack at time (3 + 1) = [ entry "ES": "Estonia", parent stack at time 3 ]	if expression state at time 3 = "begin_expr" and the expression at time 3 = entry "ES": "Estonia", then parent stack at time (3 + 1) = [ entry "ES": "Estonia", parent stack at time 3 ] (Entry Parent Property)
2	[ entry "ES": "Estonia", parent stack at time 3 ] = [ entry "ES": "Estonia", [ `{"ES": "Estonia", "MX": "Mexico"}`, [ ] ] ]	if parent stack at time 3 = [ `{"ES": "Estonia", "MX": "Mexico"}`, [ ] ], then [ entry "ES": "Estonia", parent stack at time 3 ] = [ entry "ES": "Estonia", [ `{"ES": "Estonia", "MX": "Mexico"}`, [ ] ] ] (Substitution)
3	parent stack at time (3 + 1) = [ entry "ES": "Estonia", [ `{"ES": "Estonia", "MX": "Mexico"}`, [ ] ] ]	if parent stack at time (3 + 1) = [ entry "ES": "Estonia", parent stack at time 3 ] and [ entry "ES": "Estonia", parent stack at time 3 ] = [ entry "ES": "Estonia", [ `{"ES": "Estonia", "MX": "Mexico"}`, [ ] ] ], then parent stack at time (3 + 1) = [ entry "ES": "Estonia", [ `{"ES": "Estonia", "MX": "Mexico"}`, [ ] ] ] (Transitive Property of Equality)
4	3 + 1 = 4	3 + 1 = 4 (Fixed Value Statement)
5	parent stack at time (3 + 1) = parent stack at time 4	if 3 + 1 = 4, then parent stack at time (3 + 1) = parent stack at time 4 (Substitution)
6	parent stack at time 4 = [ entry "ES": "Estonia", [ `{"ES": "Estonia", "MX": "Mexico"}`, [ ] ] ]	if parent stack at time (3 + 1) = parent stack at time 4 and parent stack at time (3 + 1) = [ entry "ES": "Estonia", [ `{"ES": "Estonia", "MX": "Mexico"}`, [ ] ] ], then parent stack at time 4 = [ entry "ES": "Estonia", [ `{"ES": "Estonia", "MX": "Mexico"}`, [ ] ] ] (Transitive Property of Equality Variation 2)

Comments

Please log in to add comments