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Proof step 15 from proof validrefs-putbyte-01 (previous step)

(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), validrefs(str, r0 ' + refs0, ty, st), is_array(str, r0, st)

Heuristic weak cut applied rule cut formula

And closed the goal!

Rule argument

[fma-arg: r0 -- i0 ' = r -- i ']

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ byteval(by) ≠ refval(r)], [CSIMPSEQ : ⊦ (st[rk, val][rk]) = val], [CSIMPFORWARD : ⊦ i < i0 ∧ i = i1 → i1 < i0], [CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ r = r0 ∧ sk = sk0], [CSIMPSEQ : ⊦ rk ≠ rk0 → (st[rk0, val][rk]) = st[rk]], [CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ ¬ ¬ (r = r0 ∧ sk = sk0)], [CSIMPSEQ : ⊦ i ' = i0 ' ↔ i = i0], [CSIMPSEQ : ⊦ 0 ≤ i ∧ i < st[r -- _length] .intval ∧ okbytearray(r, st) → st[r -- i '] ≠ refval(r1)], [CSIMPSEQ : ⊦ r ≠ r0 → ( is_array (str, r0, st[r -- sk, val]) ↔ is_array(str, r0, st))], [CSIMPSEQ : ⊦ is_array(str, r, st) → ¬ is_obj(str, r, st)])], [EXTRAFMAS : (r0 -- i0 ' = r -- i ')]]