[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 29 from proof hasSharing-put-statfield (previous step)

(st[jvmref -- sk, val][jvmref -- sks]) = refval(r0), (st[jvmref -- sk, val][jvmref -- sks0]) = refval(r0), fits(jvmref, sks0, st), fits(jvmref, sks, st), st[jvmref -- sks] .refval = jvmref ∨ st[jvmref -- sks] ≠ st[jvmref -- sks0] ⊦ sks0 = sks, sks0 = [], sks = [], r0 = jvmref

User applied rule structural induction

And obtained the following new goals

Proof step 28:
∀ st, sk, val, sks, r0. (st[jvmref -- sk, val][jvmref -- sks]) = refval(r0) ∧ (st[jvmref -- sk, val][jvmref -- sks1]) = refval(r0) ∧ fits(jvmref, sks1, st) ∧ fits(jvmref, sks, st) ∧ (st[jvmref -- sks] .refval = jvmref ∨ st[jvmref -- sks] ≠ st[jvmref -- sks1]) → sks1 = sks ∨ sks1 = [] ∨ sks = [] ∨ r0 = jvmref, (st[jvmref -- sk, val][jvmref -- sks]) = refval(r0), (st[jvmref -- sk, val][jvmref -- (sk0 + sks1)]) = refval(r0), fits(jvmref, sk0 + sks1, st), fits(jvmref, sks, st), st[jvmref -- sks] .refval = jvmref ∨ st[jvmref -- sks] ≠ st[jvmref -- (sk0 + sks1)] ⊦ sk0 + sks1 = sks, sk0 + sks1 = [], sks = [], r0 = jvmref

Rule argument

[VARWITHVARSEQSARG : sks0, ()]

Additional information

[[CONCRETESIMPRULES : ([CSIMPGEN : storekeys generated by [], +;])]]