Proof: Get Begin Expr Parent 1
Let's prove the following theorem:
if the following are true:
- expression state at time 1 = "begin_expr"
- the expression at time 1 =
{"ES": "Estonia", "MX": "Mexico"}
- parent stack at time 1 = [ ]
then parent stack at time 2 = [ {"ES": "Estonia", "MX": "Mexico"}
, [ ] ]
Proof:
Given
1 | expression state at time 1 = "begin_expr" |
---|---|
2 | the expression at time 1 = {"ES": "Estonia", "MX": "Mexico"} |
3 | parent stack at time 1 = [ ] |
# | Claim | Reason |
---|---|---|
1 | parent stack at time (1 + 1) = [ {"ES": "Estonia", "MX": "Mexico"} , parent stack at time 1 ] |
if expression state at time 1 = "begin_expr" and the expression at time 1 = {"ES": "Estonia", "MX": "Mexico"} , then parent stack at time (1 + 1) = [ {"ES": "Estonia", "MX": "Mexico"} , parent stack at time 1 ] |
2 | [ {"ES": "Estonia", "MX": "Mexico"} , parent stack at time 1 ] = [ {"ES": "Estonia", "MX": "Mexico"} , [ ] ] |
if parent stack at time 1 = [ ], then [ {"ES": "Estonia", "MX": "Mexico"} , parent stack at time 1 ] = [ {"ES": "Estonia", "MX": "Mexico"} , [ ] ] |
3 | parent stack at time (1 + 1) = [ {"ES": "Estonia", "MX": "Mexico"} , [ ] ] |
if parent stack at time (1 + 1) = [ {"ES": "Estonia", "MX": "Mexico"} , parent stack at time 1 ] and [ {"ES": "Estonia", "MX": "Mexico"} , parent stack at time 1 ] = [ {"ES": "Estonia", "MX": "Mexico"} , [ ] ], then parent stack at time (1 + 1) = [ {"ES": "Estonia", "MX": "Mexico"} , [ ] ] |
4 | 1 + 1 = 2 | 1 + 1 = 2 |
5 | parent stack at time (1 + 1) = parent stack at time 2 | if 1 + 1 = 2, then parent stack at time (1 + 1) = parent stack at time 2 |
6 | parent stack at time 2 = [ {"ES": "Estonia", "MX": "Mexico"} , [ ] ] |
if parent stack at time (1 + 1) = parent stack at time 2 and parent stack at time (1 + 1) = [ {"ES": "Estonia", "MX": "Mexico"} , [ ] ], then parent stack at time 2 = [ {"ES": "Estonia", "MX": "Mexico"} , [ ] ] |
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