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Proof step 6 from proof update-length (previous step)

validFields(r, fv ' + fis0, st), ∀ r, st, r0. validFields(r, fis0, st) → (update(r, fis0, st)[r0 -- _length]) = st[r0 -- _length] ⊦ (update(r, fis0, st)[r -- fv .1, fv .2][r0 -- _length]) = st[r0 -- _length]

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 5:
fv = sk × val, validFields(r, fv ' + fis0, st), ∀ r, st, r0. validFields(r, fis0, st) → (update(r, fis0, st)[r0 -- _length]) = st[r0 -- _length] ⊦ (update(r, fis0, st)[r -- sk, val][r0 -- _length]) = st[r0 -- _length]

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)]]