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Proof step 29 from proof validrefs-putbyte-01 (previous step)

is_array(str, r0, st) ∧ st[r0 -- _type] .type ≤ ty, (st[r -- i ', byteval(by)][r0 -- i0 ']) = refval(refs0 .first), 0 < st[r0 -- _length] .intval, 0 ≤ i0, st[r0 -- _type] .type ≤ ty, is_array(str, r0, st[r -- i ', byteval(by)]), okbytearray(r, st), validrefs(str, refs0, st[r0 -- _type] .type .type, st[r -- i ', byteval(by)]), i0 < 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, is_obj(str, r0, st), refs0 = [] ∨ (∃ i. 0 ≤ i ∧ i < st[r0 -- _length] .intval ∧ is_referencevalue(st[r0 -- i ']) ∧ refs0 .first = st[r0 -- i '] .refval ∧ validrefs(str, refs0, st[r0 -- _type] .type .type, st))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 28:
(st[r -- i ', byteval(by)][r0 -- i0 ']) = refval(refs0 .first), is_array(str, r0, st), 0 < st[r0 -- _length] .intval, 0 ≤ i0, st[r0 -- _type] .type ≤ ty, okbytearray(r, st), validrefs(str, refs0, st[r0 -- _type] .type .type, st[r -- i ', byteval(by)]), i0 < 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, refs0 = [], ∃ i1. ¬ i1 < 0 ∧ ¬ st[r0 -- _length] .intval ≤ i1 ∧ is_referencevalue(st[r0 -- i1 ']) ∧ refs0 .first = st[r0 -- i1 '] .refval ∧ validrefs(str, refs0, st[r0 -- _type] .type .type, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ is_array(str, r, st) → ¬ is_obj(str, r, st)], [CSIMPSEQ : ⊦ is_array(str, r0, st) ∧ okbytearray(r, st) → is_array (str, r0, st[r -- i ', byteval(by)])])]]