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Proof step 49 from proof junkrefs-put-nopathex-equiv (previous step)

is_array(str, r1, st) ∧ st[r1 -- _type] .type ≤ ty, is_array(str, r1, st), st[r1 -- _type] .type ≤ ty, is_valid_ref(str, r0, st), acc ≠ [] ∧ (∃ i. 0 ≤ i ∧ i < st[r1 -- _length] .intval ∧ is_referencevalue(st[r1 -- i ']) ∧ acc .first = st[r1 -- i '] .refval ∧ junkrefs(str, acc, st[r1 -- _type] .type .type, st)), ∀ str0, r2, st0, sk0, ty0, val0. ¬ path∃(str0, acc .first, r2, st0) ∧ is_valid_ref(str0, r2, st0) ∧ sk0 ≠ _type ∧ acc ≠ [] → (junkrefs(str0, acc, ty0, st0[r2 -- sk0, val0]) ↔ junkrefs(str0, acc, ty0, st0)) ⊦ r0 = r1, r1 = jvmref, sk = _type, path∃(str, r1, r0, st), junkrefs(str, r1 ' + acc, ty, st[r0 -- sk, val])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 48:
acc .first = st[r1 -- i '] .refval, is_array(str, r1, st), st[r1 -- _type] .type ≤ ty, is_valid_ref(str, r0, st), i < st[r1 -- _length] .intval, is_referencevalue(st[r1 -- i ']), junkrefs(str, acc, st[r1 -- _type] .type .type, st), 0 ≤ i, 0 < st[r1 -- _length] .intval, ∀ str0, r, st0, sk0, ty0, val0. ¬ path∃(str0, acc .first, r, st0) ∧ is_valid_ref(str0, r, st0) ∧ sk0 ≠ _type → (junkrefs(str0, acc, ty0, st0[r -- sk0, val0]) ↔ junkrefs(str0, acc, ty0, st0)) ⊦ r0 = r1, r1 = jvmref, sk = _type, acc = [], path∃(str, r1, r0, st), junkrefs(str, r1 ' + acc, ty, st[r0 -- sk, val])

Rule argument

[emptyarg]

Additional information

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