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Proof step 10 from proof addarray-mklist-05 (previous step)

addarray(r, ty, mklist(initial_value(ty), m), st) = (addarray(r, initial_value(ty), n→i(m), st)[r -- _type, typeval(mkarraytype(ty))][r -- _length, intval(n→i(m))]) ⊦ (addarray(r, initial_value(ty), n→i(m), st)[r -- _type, typeval(mkarraytype(ty))][r -- n→i(m) ', initial_value(ty)] [r -- _length, intval(n→i(m) + 1) ] ) = (addarray(r, initial_value(ty), n→i(m), st)[r -- n→i(m) ', initial_value(ty)][r -- _type, typeval(mkarraytype(ty))] [r -- _length, intval(n→i(m) + 1) ] )

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ rk ≠ rk0 → (st[rk0, val][rk, val0]) = (st[rk, val0][rk0, val])

Rule argument

[speclemmaarg: ,rk ≠ rk0 → (st[rk0, val][rk, val0]) = (st[rk, val0][rk0, val]) ,[val0, rk, val, rk0, st] → [initial_value(ty), r -- n→i(m) ', typeval(mkarraytype(ty)), r -- _type, addarray(r, initial_value(ty), n→i(m), st)] ,F ,store ,javastore ,rew ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ r = r0 ∧ sk = sk0], [CSIMPSEQ : ⊦ _type ≠ i '])], [EXTRATERMS : (initial_value(ty), r -- n→i(m) ', typeval(mkarraytype(ty)), r -- _type, addarray(r, initial_value(ty), n→i(m), st))]]