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Proof step 49 from proof validrefs-lastelem (previous step)

is_array(str, r1, st) ∧ st[r1 -- _type] .type ≤ ty0, st[r0 -- mkfs(class, ty0, fieldvar) '] = refval(r1), st[r0 -- mkfs(class0, ty1, fieldvar0) '] = refval(r1), is_array(str, r1, st), is_obj(str, r0, st), st[r0 -- _type] .type ≤ ty, mkfs(class, ty0, fieldvar) ' ∈ instfields(st[r0 -- _type] .type .class), validrefs(str, r1 ' + refs0 + r ', ty0, st), mkfs(class0, ty1, fieldvar0) ' ∈ instfields(st[r0 -- _type] .type .class), st[r1 -- _type] .type ≤ ty0, st[r1 -- _type] .type ≤ ty1, refs0 = [] ∨ 0 ≤ i ∧ i < st[r1 -- _length] .intval ∧ is_referencevalue(st[r1 -- i ']) ∧ refs0 .first = st[r1 -- i '] .refval ∧ validrefs(str, refs0, st[r1 -- _type] .type .type, st) ⊦ r0 = jvmref, r1 = jvmref, has_reffield((r1 ' + refs0) .last, st), refs0 = [] ∨ (∃ i. 0 ≤ i ∧ i < st[r1 -- _length] .intval ∧ is_referencevalue(st[r1 -- i ']) ∧ refs0 .first = st[r1 -- i '] .refval ∧ validrefs(str, refs0, st[r1 -- _type] .type .type, st))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 48:
st[r0 -- mkfs(class, ty0, fieldvar) '] = refval(r1), st[r0 -- mkfs(class0, ty1, fieldvar0) '] = refval(r1), refs0 .first = st[r1 -- i '] .refval, is_array(str, r1, st), is_obj(str, r0, st), st[r0 -- _type] .type ≤ ty, mkfs(class, ty0, fieldvar) ' ∈ instfields(st[r0 -- _type] .type .class), validrefs(str, r1 ' + refs0 + r ', ty0, st), mkfs(class0, ty1, fieldvar0) ' ∈ instfields(st[r0 -- _type] .type .class), st[r1 -- _type] .type ≤ ty0, st[r1 -- _type] .type ≤ ty1, i < st[r1 -- _length] .intval, is_referencevalue(st[r1 -- i ']), validrefs(str, refs0, st[r1 -- _type] .type .type, st), 0 ≤ i, 0 < st[r1 -- _length] .intval ⊦ r0 = jvmref, r1 = jvmref, refs0 = [], has_reffield(refs0 .last, st), ∃ i0. ¬ i0 < 0 ∧ ¬ st[r1 -- _length] .intval ≤ i0 ∧ is_referencevalue(st[r1 -- i0 ']) ∧ refs0 .first = st[r1 -- i0 '] .refval

Rule argument

[emptyarg]

Additional information

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