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Proof step 12 from proof lookup-list-put-ex (previous step)

r -- sk0 = r0 -- sk, ∀ st0, r1, sk1, val0, r2. (st0[r1 -- sk1, val0][r2 -- sks0]) ≠ st0[r2 -- sks0] → (∃ sks, sks1. sks0 = sks + sk1 ' + sks1 ∧ st0[r2 -- sks] .refval = r1) ⊦ sks0 = [], (st[r0 -- sk, val][(st[r0 -- sk, val][r -- sk0]) .refval -- sks0]) = st[r -- (sk0 ' + sks0)], ∃ sks, sks1. sk0 ' + sks0 = sks + sk ' + sks1 ∧ st[r -- sks] .refval = r0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 11:
∀ st0, r1, sk1, val0, r2. (st0[r1 -- sk1, val0][r2 -- sks0]) ≠ st0[r2 -- sks0] → (∃ sks, sks1. sks0 = sks + sk1 ' + sks1 ∧ st0[r2 -- sks] .refval = r1) ⊦ sks0 = [], (st[r0 -- sk, val][val .refval -- sks0]) = st[r0 -- (sk ' + sks0)], ∃ sks, sks1. sk ' + sks0 = sks + sk ' + sks1 ∧ st[r0 -- sks] .refval = r0

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : store, javastore, At-same, ⊦ (st[rk, val][rk]) = val], [CSIMPNAMEDSEQ : refkey, , inj, ⊦ r -- sk = r0 -- sk0 ↔ r = r0 ∧ sk = sk0])]]