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Proof step 57 from proof validrefs-subset-01 (previous step)

r0 -- _type ∈ st ∧ st ⊆ st0, st[r0 -- i '] = refval(r), validrefs(str, r ' + refs, st[r0 -- _type] .type .type, st), i < st[r0 -- _length] .intval, st[r0 -- _type] .type ≤ ty, st ⊆ st0, is_array(str, r0, st), st[r0 -- _type] .type ≤ ty, 0 < st[r0 -- _length] .intval, 0 ≤ i, ∀ str0, ty0, st1, st2. validrefs(str0, r ' + refs, ty0, st1) ∧ st1 ⊆ st2 ∧ ¬ junkref(str0, r, st1) → validrefs(str0, r ' + refs, ty0, st2) ⊦ r0 = jvmref, junkref(str, r0, st), ∃ i0. ¬ i0 < 0 ∧ ¬ st0[r0 -- _length] .intval ≤ i0 ∧ is_referencevalue(st0[r0 -- i0 ']) ∧ r = st0[r0 -- i0 '] .refval ∧ validrefs(str, st0[r0 -- i0 '] .refval ' + refs, st[r0 -- _type] .type .type, st0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 56:
st[r0 -- i '] = refval(r), r0 -- _type ∈ st, validrefs(str, r ' + refs, st[r0 -- _type] .type .type, st), i < st[r0 -- _length] .intval, st ⊆ st0, is_array(str, r0, st), st[r0 -- _type] .type ≤ ty, 0 < st[r0 -- _length] .intval, 0 ≤ i, r0 ∈ st, ∀ str0, ty0, st1, st2. validrefs(str0, r ' + refs, ty0, st1) ∧ st1 ⊆ st2 ∧ ¬ junkref(str0, r, st1) → validrefs(str0, r ' + refs, ty0, st2) ⊦ r0 = jvmref, junkref(str, r0, st), ∃ i0. ¬ i0 < 0 ∧ ¬ st0[r0 -- _length] .intval ≤ i0 ∧ is_referencevalue(st0[r0 -- i0 ']) ∧ r = st0[r0 -- i0 '] .refval ∧ validrefs(str, st0[r0 -- i0 '] .refval ' + refs, st[r0 -- _type] .type .type, st0)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ r -- sk ∈ st → r ∈ st], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])]]