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Proof step 15 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, (fv + fis0)[sk, val], st) = (update(r, fv + fis0, st)[r -- sk, val])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
⊦ update(r, fv ' + fis, st) = (update(r, fis, st)[r -- fv .1, fv .2])
Proof step 14:
∀ r, sk, val, st. update(r, fis0[sk, val], st) = (update(r, fis0, st)[r -- sk, val]) ⊦ update(r, (fv ' + fis0)[sk, val], st) = (update(r, fis0, st)[r -- fv .1, fv .2][r -- sk, val])

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (fis + fis0) + fis1 = fis + fis0 + fis1], [CSIMPSEQ : ⊦ fv + fis = fv ' + fis])]]