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Proof step 49 from proof validrefs-putbyte (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 32:
⊦ is_array(str, r, st) ∧ st[r -- _type] .type ≤ ty → ( validrefs(str, r ' + refs, ty, st) ↔ refs = [] ∨ (∃ i. 0 ≤ i ∧ i < st[r -- _length] .intval ∧ is_referencevalue(st[r -- i ']) ∧ refs .first = st[r -- i '] .refval ∧ validrefs(str, refs, st[r -- _type] .type .type, st)))
Proof step 33:
¬ (is_array(str, r0, st[r -- i ', byteval(by)]) ∧ (st[r -- i ', byteval(by)][r0 -- _type]) .type ≤ ty), st[r0 -- i0 '] = refval(refs0 .first), 0 < st[r0 -- _length] .intval, 0 ≤ i0, st[r0 -- _type] .type ≤ ty, okbytearray(r, st), is_array(str, r0, st), validrefs(str, refs0, st[r0 -- _type] .type .type, st), i0 < st[r0 -- _length] .intval, ∀ by, i, ty, str, st, r, refs1. # refs1 < # (r0 ' + refs0) → (okbytearray(r, st) ∧ validrefs(str, refs1, ty, st) → validrefs(str, refs1, ty, st[r -- i ', byteval(by)])) ⊦ r0 = jvmref, validrefs(str, r0 ' + refs0, ty, st[r -- i ', byteval(by)])
Proof step 48:
is_array(str, r0, st[r -- i ', byteval(by)]) ∧ (st[r -- i ', byteval(by)][r0 -- _type]) .type ≤ ty, st[r0 -- i0 '] = refval(refs0 .first), 0 < st[r0 -- _length] .intval, 0 ≤ i0, st[r0 -- _type] .type ≤ ty, okbytearray(r, st), is_array(str, r0, st), validrefs(str, refs0, st[r0 -- _type] .type .type, st), i0 < st[r0 -- _length] .intval, ∀ by, i, ty, str, st, r, refs1. # refs1 < # (r0 ' + refs0) → (okbytearray(r, st) ∧ validrefs(str, refs1, ty, st) → validrefs(str, refs1, ty, st[r -- i ', byteval(by)])) ⊦ r0 = jvmref, refs0 = [] ∨ (∃ i0. 0 ≤ i0 ∧ i0 < (st[r -- i ', byteval(by)][r0 -- _length]) .intval ∧ is_referencevalue(st[r -- i ', byteval(by)][r0 -- i0 ']) ∧ refs0 .first = (st[r -- i ', byteval(by)][r0 -- i0 ']) .refval ∧ validrefs(str, refs0, (st[r -- i ', byteval(by)][r0 -- _type]) .type .type, st[r -- i ', byteval(by)]))

Rule argument

[crewrite-arg: validrefs-array , F , [st, ty, refs, r, str] → [st[r -- i ', byteval(by)], ty, refs0, r0, str] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st[r -- i ', byteval(by)], ty, refs0, r0, str)]]