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Proof step 52 from proof hasSharing-pathex (previous step)

is_array(str, r, st) ∧ st[r -- _type] .type ≤ st[r -- _type] .type, is_array(str, r, st), hasSharing(r0, st), refs1 + r0 ' = [] ∨ (∃ i. 0 ≤ i ∧ i < st[r -- _length] .intval ∧ is_referencevalue(st[r -- i ']) ∧ (refs1 + r0 ') .first = st[r -- i '] .refval ∧ validrefs(str, refs1 + r0 ', st[r -- _type] .type .type, st)), ∀ st, r, str, refs. # refs < # (refs1 + r0 ') → (validrefs(str, r ' + refs, st[r -- _type] .type, st) ∧ hasSharing(refs .last, st) → refs = [] ∨ hasSharing(r, st)) ⊦ r = jvmref, hasSharing(r, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 51:
(refs1 + r0 ') .first = st[r -- i '] .refval, is_array(str, r, st), hasSharing(r0, st), i < st[r -- _length] .intval, is_referencevalue(st[r -- i ']), validrefs(str, refs1 + r0 ', st[r -- _type] .type .type, st), 0 ≤ i, 0 < st[r -- _length] .intval, ∀ st, r, str, refs. # refs < # (refs1 + r0 ') → (validrefs(str, r ' + refs, st[r -- _type] .type, st) ∧ hasSharing(refs .last, st) → refs = [] ∨ hasSharing(r, st)) ⊦ r = jvmref, hasSharing(r, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPFORWARD : ⊦ i < j ∧ 0 ≤ i → 0 < j], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ r ' ≠ []], [CSIMPSEQ : ⊦ ¬ refs + refs0 ≠ [] ↔ refs = [] ∧ refs0 = []], [CSIMPSEQ : ⊦ ty ≤ ty])]]