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Proof step 25 from proof validrefs-putbyte-01 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 24:
(st[r -- i ', byteval(by)][r0 -- i0 ']) = refval(r1), i0 < st[r0 -- _length] .intval, is_array(str, r0, st), 0 < st[r0 -- _length] .intval, 0 ≤ i0, st[r0 -- _type] .type ≤ ty, okbytearray(r, st), validrefs(str, r1 ' + refs, st[r0 -- _type] .type .type, st[r -- i ', byteval(by)]), ∀ by, i, ty, str, st, r, refs1. # refs1 < # (r0 ' + (r1 + refs)) → (okbytearray(r, st) ∧ validrefs(str, refs1, ty, st[r -- i ', byteval(by)]) → validrefs(str, refs1, ty, st)) ⊦ r0 = jvmref, is_referencevalue(st[r0 -- i0 ']) ∧ r1 = st[r0 -- i0 '] .refval ∧ validrefs(str, st[r0 -- i0 '] .refval ' + refs, st[r0 -- _type] .type .type, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i < j → (¬ ¬ j ≤ i ↔ false)], [CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)])]]