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Proof step 13 from proof keys-at (previous step)

n < # fis ⊦ (fis .keys)[n] = fis[n] .1, fis = []

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 12:
fis[n] = sk × val, n < # fis ⊦ (fis .keys)[n] = sk, fis = []

Rule argument

[x0lemmaarg: spec-name: pair instance-name: fieldinit lemma-name: elim antecedent: succedent: sk = fv .1 ∧ val = fv .2 ↔ fv = sk × val substlist: [fv, sk, val] → [fis[n], sk, val] add preconditions?: F is rewrite lemma?: F current spec?: F rotate lemma?: T replace all?: T paths: () dummy: () ]

Additional information

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