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author soto@cr.ie.u-ryukyu.ac.jp
date Tue, 08 Sep 2020 18:38:08 +0900
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proof1 : HTProof initCond program termCond
proof1 =
  SeqRule {λ e → true} ( PrimRule empty-case )
    $ SeqRule {λ e →  Equal (varn e) 10} ( PrimRule lemma1   )
    $ WeakeningRule {λ e → (Equal (varn e) 10) ∧ (Equal (vari e) 0)}  lemma2 (
      WhileRule {_} {λ e → Equal ((varn e) + (vari e)) 10}
        $ SeqRule (PrimRule {λ e →  whileInv e  ∧ lt zero (varn e) } lemma3 )
        $ PrimRule {whileInv'} {_} {whileInv}  lemma4 ) lemma5