Proof: Do Expr At Unchanged 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"}

then the expression at time 2 = {"ES": "Estonia", "MX": "Mexico"}

Proof:

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Given
1 expression state at time 1 = "begin_expr"
2 the expression at time 1 = {"ES": "Estonia", "MX": "Mexico"}
Proof Table
# Claim Reason
1 the expression at time (1 + 1) = the expression at time 1 if expression state at time 1 = "begin_expr", then the expression at time (1 + 1) = the expression at time 1
2 the expression at time (1 + 1) = {"ES": "Estonia", "MX": "Mexico"} if the expression at time (1 + 1) = the expression at time 1 and the expression at time 1 = {"ES": "Estonia", "MX": "Mexico"}, then the expression at time (1 + 1) = {"ES": "Estonia", "MX": "Mexico"}
3 1 + 1 = 2 1 + 1 = 2
4 the expression at time (1 + 1) = the expression at time 2 if 1 + 1 = 2, then the expression at time (1 + 1) = the expression at time 2
5 the expression at time 2 = {"ES": "Estonia", "MX": "Mexico"} if the expression at time (1 + 1) = the expression at time 2 and the expression at time (1 + 1) = {"ES": "Estonia", "MX": "Mexico"}, then the expression at time 2 = {"ES": "Estonia", "MX": "Mexico"}

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