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Proof step 32 from proof validrefs-putbyte-01 (previous step)

refs0 .first = (st[r -- i ', byteval(by)][r0 -- i0 ']) .refval, i0 < st[r0 -- _length] .intval, is_referencevalue(st[r -- i ', byteval(by)][r0 -- i0 ']), validrefs(str, refs0, st[r0 -- _type] .type .type, st[r -- i ', byteval(by)]), okbytearray(r, st), is_array(str, r0, st[r -- i ', byteval(by)]), st[r0 -- _type] .type ≤ ty, 0 ≤ i0, 0 < st[r0 -- _length] .intval, ∀ by, i, ty, str, st, r, refs1. # refs1 < # (r0 ' + refs0) → (okbytearray(r, st) ∧ validrefs(str, refs1, ty, st[r -- i ', byteval(by)]) → validrefs(str, refs1, ty, st)) ⊦ r0 = jvmref, validrefs(str, r0 ' + refs0, ty, st), is_obj(str, r0, st)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 31:
(st[r -- i ', byteval(by)][r0 -- i0 ']) = refval(r1), refs0 .first = r1, i0 < st[r0 -- _length] .intval, is_referencevalue(st[r -- i ', byteval(by)][r0 -- i0 ']), validrefs(str, refs0, st[r0 -- _type] .type .type, st[r -- i ', byteval(by)]), okbytearray(r, st), is_array(str, r0, st[r -- i ', byteval(by)]), st[r0 -- _type] .type ≤ ty, 0 ≤ i0, 0 < st[r0 -- _length] .intval, ∀ by, i, ty, str, st, r, refs1. # refs1 < # (r0 ' + refs0) → (okbytearray(r, st) ∧ validrefs(str, refs1, ty, st[r -- i ', byteval(by)]) → validrefs(str, refs1, ty, st)) ⊦ r0 = jvmref, validrefs(str, r0 ' + refs0, ty, st), is_obj(str, r0, st)

Rule argument

[speclemmaarg: ,is_referencevalue(val) → (r = val .refval ↔ val = refval(r)) ,[val, r] → [st[r -- i ', byteval(by)][r0 -- i0 '], r1] ,T ,javavalue , ,elim-13 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ is_referencevalue(val) → ( r = val .refval ↔ val = refval(r))])], [EXTRATERMS : (st[r -- i ', byteval(by)][r0 -- i0 '], r1)]]