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Proof step 50 from proof validrefs-junkrefs-01 (previous step)

is_array(str, r, st) ∧ st[r -- _type] .type ≤ ty, acc + refs0 = r0 ' + refs, st[r -- i '] = refval(r0), is_array(str, r, st), i < st[r -- _length] .intval, junkrefs(str, acc + refs0, st[r -- _type] .type .type, st), st[r -- _type] .type ≤ ty, 0 ≤ i, 0 < st[r -- _length] .intval, ∀ str, refs0, ty, st. junkrefs(str, acc + refs0, ty, st) → junkrefs(str, acc, ty, st) ∨ validrefs(str, acc, ty, st) ⊦ r = jvmref, acc + refs0 = [], acc ≠ [] ∧ (∃ i. 0 ≤ i ∧ i < st[r -- _length] .intval ∧ is_referencevalue(st[r -- i ']) ∧ acc .first = st[r -- i '] .refval ∧ junkrefs(str, acc, st[r -- _type] .type .type, st)), validrefs(str, r ' + acc, ty, st), ¬ r0 ∈ acc ∧ ¬ r0 ∈ refs0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 49:
acc + refs0 = r0 ' + refs, st[r -- i '] = refval(r0), is_array(str, r, st), i < st[r -- _length] .intval, junkrefs(str, acc + refs0, st[r -- _type] .type .type, st), st[r -- _type] .type ≤ ty, 0 ≤ i, 0 < st[r -- _length] .intval, ∀ str, refs0, ty, st. junkrefs(str, acc + refs0, ty, st) → junkrefs(str, acc, ty, st) ∨ validrefs(str, acc, ty, st) ⊦ r = jvmref, acc + refs0 = [], validrefs(str, r ' + acc, ty, st), ¬ r0 ∈ acc ∧ ¬ r0 ∈ refs0, acc ≠ [] ∧ (∃ i0. ¬ i0 < 0 ∧ ¬ st[r -- _length] .intval ≤ i0 ∧ is_referencevalue(st[r -- i0 ']) ∧ acc .first = st[r -- i0 '] .refval ∧ junkrefs(str, acc, st[r -- _type] .type .type, st))

Rule argument

[emptyarg]

Additional information

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