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Proof step 41 from proof validrefs-putbyte (previous step)

st[r0 -- i0 '] = refval(r1), validrefs(str, (st[r -- i ', byteval(by)][r0 -- i0 ']) .refval ' + refs, st[r0 -- _type] .type .type, st[r -- i ', byteval(by)]), i0 < st[r0 -- _length] .intval, is_array(str, r0, st[r -- i ', byteval(by)]), st[r0 -- _type] .type ≤ ty, 0 < st[r0 -- _length] .intval, 0 ≤ i0, okbytearray(r, st), is_array(str, r0, st), validrefs(str, r1 ' + refs, st[r0 -- _type] .type .type, st), ∀ by, i, ty, str, st, r, refs1. # refs1 < # (r0 ' + (r1 + refs)) → (okbytearray(r, st) ∧ validrefs(str, refs1, ty, st) → validrefs(str, refs1, ty, st[r -- i ', byteval(by)])) ⊦ r0 = jvmref, is_referencevalue(st[r -- i ', byteval(by)][r0 -- i0 ']) ∧ r1 = (st[r -- i ', byteval(by)][r0 -- i0 ']) .refval

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 37:
⊦ sk ≠ sk0 → (st[r -- sk, val][r0 -- sk0]) = st[r0 -- sk0]
Proof step 40:
¬ i ' ≠ i0 ', st[r0 -- i0 '] = refval(r1), validrefs(str, (st[r -- i ', byteval(by)][r0 -- i0 ']) .refval ' + refs, st[r0 -- _type] .type .type, st[r -- i ', byteval(by)]), i0 < st[r0 -- _length] .intval, is_array(str, r0, st[r -- i ', byteval(by)]), st[r0 -- _type] .type ≤ ty, 0 < st[r0 -- _length] .intval, 0 ≤ i0, okbytearray(r, st), is_array(str, r0, st), validrefs(str, r1 ' + refs, st[r0 -- _type] .type .type, st), ∀ by, i, ty, str, st, r, refs1. # refs1 < # (r0 ' + (r1 + refs)) → (okbytearray(r, st) ∧ validrefs(str, refs1, ty, st) → validrefs(str, refs1, ty, st[r -- i ', byteval(by)])) ⊦ r0 = jvmref, is_referencevalue(st[r -- i ', byteval(by)][r0 -- i0 ']) ∧ r1 = (st[r -- i ', byteval(by)][r0 -- i0 ']) .refval

Rule argument

[speclemmaarg: ,sk ≠ sk0 → (st[r -- sk, val][r0 -- sk0]) = st[r0 -- sk0] ,[sk0, r0, val, sk, r, st] → [i0 ', r0, byteval(by), i ', r, st] ,F ,javastore , ,at-other-16 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i ' = i0 ' ↔ i = i0], [CSIMPSEQ : ⊦ refval(r) .refval = r], [CSIMPSEQ : ⊦ is_referencevalue(refval(r))])], [EXTRATERMS : (i0 ', r0, byteval(by), i ', r, st)]]