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Proof step 13 from proof update-putfis-sw (previous step)

∀ r, sk, val, st. update(r, fis0[sk, val], st) = (update(r, fis0, st)[r -- sk, val]) ⊦ update(r, ((sk0 × val0) ' + fis0)[sk, val], st) = (update(r, fis0, st)[r -- (sk0 × val0) .1, (sk0 × val0) .2][r -- sk, val])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
∀ r, sk, val, st. update(r, fis0[sk, val], st) = (update(r, fis0, st)[r -- sk, val]) ⊦ update(r, ((sk0 × val0) ' + fis0)[sk, val], st) = (update(r, fis0, st)[r -- sk0, val0][r -- sk, val])

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (sk × val) .2 = val], [CSIMPSEQ : ⊦ (sk × val) .1 = sk])]]