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Proof step 58 from proof hassharing-validrefs-dups (previous step)

is_array(str, r, st) ∧ st[r -- _type] .type ≤ st[r -- _type] .type, hasSharing(r1, st), validrefs(str, r1 ' + refs1, st[r1 -- _type] .type, st), r1 ' + refs1 = [] ∨ (∃ i. 0 ≤ i ∧ i < st[r -- _length] .intval ∧ is_referencevalue(st[r -- i ']) ∧ (r1 ' + refs1) .first = st[r -- i '] .refval ∧ validrefs(str, r1 ' + refs1, st[r -- _type] .type .type, st)), is_array(str, r, st), ∀ st, str, refs, r0. # (r0 ' + refs) < # (r ' + (r1 + refs1)) → (validrefs(str, r0 ' + refs, st[r0 -- _type] .type, st) → hasSharing(r0, st) ∨ ¬ r0 ∈ refs ∧ ¬ dups(refs)) ⊦ r = jvmref, hasSharing(r, st), r ∈ refs1, ¬ r1 ∈ refs1 ∧ ¬ dups(refs1)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 57:
0 < st[r -- _length] .intval, 0 ≤ i, validrefs(str, st[r -- i '] .refval ' + refs1, st[r -- _type] .type .type, st), is_referencevalue(st[r -- i ']), i < st[r -- _length] .intval, is_array(str, r, st), validrefs(str, st[r -- i '] .refval ' + refs1, st[st[r -- i '] .refval -- _type] .type, st), hasSharing(st[r -- i '] .refval, st), ∀ st0, str, refs, r0. # (r0 ' + refs) < # (r ' + (st[r -- i '] .refval + refs1)) → (validrefs(str, r0 ' + refs, st0[r0 -- _type] .type, st0) → hasSharing(r0, st0) ∨ ¬ r0 ∈ refs ∧ ¬ dups(refs)) ⊦ r = jvmref, r ∈ refs1, hasSharing(r, st), ¬ st[r -- i '] .refval ∈ refs1 ∧ ¬ dups(refs1)

Rule argument

[emptyarg]

Additional information

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