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Proof step 52 from proof validrefs-lastelem (previous step)

is_array(str, r1, st), st[r0 -- mkfs(class, ty0, fieldvar) '] = refval(r1), st[r0 -- mkfs(class0, ty1, fieldvar0) '] = refval(r1), 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), validrefs(str, r1 ' + refs0, ty1, st), st[r1 -- _type] .type ≤ ty0, st[r1 -- _type] .type ≤ ty1 ⊦ r0 = jvmref, r1 = jvmref, has_reffield((r1 ' + refs0) .last, st), validrefs(str, r1 ' + refs0, ty0, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 42:
⊦ is_array(str, r, st) ∧ st[r -- _type] .type ≤ ty → ( validrefs(str, r ' + refs, ty, st) ↔ refs = [] ∨ (∃ i. 0 ≤ i ∧ i < st[r -- _length] .intval ∧ is_referencevalue(st[r -- i ']) ∧ refs .first = st[r -- i '] .refval ∧ validrefs(str, refs, st[r -- _type] .type .type, st)))
Proof step 51:
is_array(str, r1, st) ∧ st[r1 -- _type] .type ≤ ty1, is_array(str, r1, st), st[r0 -- mkfs(class, ty0, fieldvar) '] = refval(r1), st[r0 -- mkfs(class0, ty1, fieldvar0) '] = refval(r1), 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), 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)), st[r1 -- _type] .type ≤ ty0, st[r1 -- _type] .type ≤ ty1 ⊦ r0 = jvmref, r1 = jvmref, has_reffield((r1 ' + refs0) .last, st), validrefs(str, r1 ' + refs0, ty0, st)

Rule argument

[crewrite-arg: validrefs-array , F , [st, ty, refs, r, str] → [st, ty1, refs0, r1, str] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])], [EXTRATERMS : (st, ty1, refs0, r1, str)]]