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Proof step 15 from proof update-ex-nodups (previous step)

∀ r, st. ∃ fis1. ¬ dups(fis1 .keys) ∧ update(r, fis0, st) = update(r, fis1, st) ∧ fis1 ⊆ fis0 ⊦ ∃ fis. ¬ dups(fis .keys) ∧ (update(r, fis0, st)[r -- fv .1, fv .2]) = update(r, fis, st) ∧ fis ⊆ fv ' + fis0

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 14:
fv = sk × val, ∀ r, st. ∃ fis1. ¬ dups(fis1 .keys) ∧ update(r, fis0, st) = update(r, fis1, st) ∧ fis1 ⊆ fis0 ⊦ ∃ fis. ¬ dups(fis .keys) ∧ (update(r, fis0, st)[r -- sk, val]) = update(r, fis, st) ∧ fis ⊆ fv ' + fis0

Rule argument

[speclemmaarg: ,sk = fv .1 ∧ val = fv .2 ↔ fv = sk × val ,[fv, sk, val] → [fv, sk, val] ,T ,pair ,fieldinit ,elim ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ sk = fv .1 ∧ val = fv .2 ↔ fv = sk × val])], [EXTRATERMS : (fv, sk, val)]]