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Proof step 47 from proof validrefs-subset-01 (previous step)

st[r0 -- i '] = refval(r), r0 ∈ st, 0 ≤ i, 0 < st[r0 -- _length] .intval, st[r0 -- _type] .type ≤ ty, is_array(str, r0, st), st ⊆ st0, i < st[r0 -- _length] .intval, validrefs(str, r ' + refs, st[r0 -- _type] .type .type, st), r0 -- _type ∈ st, r0 -- _length ∈ st, r0 -- i ' ∈ 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, validrefs(str, r ' + refs, st[r0 -- _type] .type .type, st0), ¬ i < 0 ∧ ¬ st[r0 -- _length] .intval ≤ i ∧ is_referencevalue(st[r0 -- i ']) ∧ st[r0 -- i '] .refval ≠ jvmref ∧ (¬ st[st[r0 -- i '] .refval -- _type] .type ≤ st[r0 -- _type] .type .type ∨ junkref(str, st[r0 -- i '] .refval, st))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 45:
⊦ validrefs(str, jvmref ' + refs, ty, st) ↔ refs = []
Proof step 46:
st[r0 -- i '] = refval(r), r0 -- i ' ∈ st, r0 -- _length ∈ st, 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, st[r -- _type] .type ≤ st[r0 -- _type] .type .type, ∀ str0, ty0, st1, st2. validrefs(str0, r ' + refs, ty0, st1) ∧ st1 ⊆ st2 ∧ ¬ junkref(str0, r, st1) → validrefs(str0, r ' + refs, ty0, st2) ⊦ r0 = jvmref, r = jvmref, validrefs(str, r ' + refs, st[r0 -- _type] .type .type, st0), junkref(str, r, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ refval(r) .refval = r], [CSIMPSEQ : ⊦ is_referencevalue(refval(r))], [CSIMPSEQ : ⊦ i < j → (¬ ¬ j ≤ i ↔ false)], [CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])]]