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Proof step 29 from proof validrefs-addobj-junkref (previous step)

is_array(str, r1, st), st[r1 -- i '] = refval(r2), is_array(str, r1, st), newref(r, st), st[r1 -- _type] .type ≤ ty0, i < st[r1 -- _length] .intval, validrefs(str, r2 ' + refs, st[r1 -- _type] .type .type, addobj(r, class, fis, st)), 0 ≤ i, 0 < st[r1 -- _length] .intval, ∀ str0, ty, r0, class0, fis0, st0. validrefs(str0, r2 ' + refs, ty, addobj(r0, class0, fis0, st0)) ∧ newref(r0, st0) ∧ (r0 = r2 ∨ r0 ∈ refs) → junkref(str0, r2, st0) ⊦ r1 = jvmref, r = jvmref, r = r1, ∃ i. 0 ≤ i ∧ i < st[r1 -- _length] .intval ∧ is_referencevalue(st[r1 -- i ']) ∧ st[r1 -- i '] .refval ≠ jvmref ∧ (¬ st[st[r1 -- i '] .refval -- _type] .type ≤ st[r1 -- _type] .type .type ∨ junkref(str, st[r1 -- i '] .refval, st)), r ≠ r2 ∧ ¬ r ∈ refs

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 28:
st[r1 -- i '] = refval(r2), is_array(str, r1, st), newref(r, st), st[r1 -- _type] .type ≤ ty0, i < st[r1 -- _length] .intval, validrefs(str, r2 ' + refs, st[r1 -- _type] .type .type, addobj(r, class, fis, st)), 0 ≤ i, 0 < st[r1 -- _length] .intval, ∀ str0, ty, r0, class0, fis0, st0. validrefs(str0, r2 ' + refs, ty, addobj(r0, class0, fis0, st0)) ∧ newref(r0, st0) ∧ (r0 = r2 ∨ r0 ∈ refs) → junkref(str0, r2, st0) ⊦ r1 = jvmref, r = jvmref, r = r1, r ≠ r2 ∧ ¬ r ∈ refs, ∃ i0. ¬ i0 < 0 ∧ ¬ st[r1 -- _length] .intval ≤ i0 ∧ is_referencevalue(st[r1 -- i0 ']) ∧ st[r1 -- i0 '] .refval ≠ jvmref ∧ (¬ st[st[r1 -- i0 '] .refval -- _type] .type ≤ st[r1 -- _type] .type .type ∨ junkref(str, st[r1 -- i0 '] .refval, st))

Rule argument

[emptyarg]

Additional information

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