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Proof step 56 from proof validrefs-junkrefs-01 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 55:
(acc + refs0) .first = st[r -- i '] .refval, is_array(str, r, st), i < st[r -- _length] .intval, is_referencevalue(st[r -- i ']), 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 = [], junkrefs(str, r ' + acc, ty, st), validrefs(str, r ' + acc, ty, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPFORWARD : ⊦ i < j ∧ 0 ≤ i → 0 < j])]]