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Proof step 12 from proof putarray-add-butlast (previous step)

is_fskey(_length) ⊦ (addarray(r, vals, 0, st[r -- _type, typeval(mkarraytype(ty))][r -- _length, intval(n→i(# vals) + 1)])[r -- n→i(# vals) ', initial_value(ty)]) = (addarray(r, vals, 0, st[r -- _type, typeval(mkarraytype(ty))])[r -- _length, intval(n→i(# vals))][r -- n→i(# vals) ', initial_value(ty)] [r -- _length, intval(n→i(# vals) + 1) ] )

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ rk ≠ rk0 → (st[rk0, val][rk, val0]) = (st[rk, val0][rk0, val])
Proof step 11:
r -- _length ≠ r -- n→i(# vals) ', is_fskey(_length) ⊦ (addarray(r, vals, 0, st[r -- _type, typeval(mkarraytype(ty))][r -- _length, intval(n→i(# vals) + 1)])[r -- n→i(# vals) ', initial_value(ty)]) = (addarray(r, vals, 0, st[r -- _type, typeval(mkarraytype(ty))])[r -- _length, intval(n→i(# vals))][r -- _length, intval(n→i(# vals) + 1)] [r -- n→i(# vals) ', initial_value(ty) ] )

Rule argument

[speclemmaarg: ,rk ≠ rk0 → (st[rk0, val][rk, val0]) = (st[rk, val0][rk0, val]) ,[val0, rk, val, rk0, st] → [intval(n→i(# vals) + 1), r -- _length, initial_value(ty), r -- n→i(# vals) ', addarray(r, vals, 0, st[r -- _type, typeval(mkarraytype(ty))]) [r -- _length, intval(n→i(# vals)) ]] ,F ,store ,javastore ,rew ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ r = r0 ∧ sk = sk0], [CSIMPSEQ : ⊦ _length ≠ i '])], [EXTRATERMS : (intval(n→i(# vals) + 1), r -- _length, initial_value(ty), r -- n→i(# vals) ', addarray (r, vals, 0, st[r -- _type, typeval(mkarraytype(ty))]) [r -- _length, intval(n→i(# vals)) ])]]