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Proof step 149 from proof validref-refs-last-valid-subset (previous step)

validref(str, r, st[r -- _type] .type, st), st ⊆ st0, validrefs(str, (r0 ' + acc) + r1 ', ty, st0), is_valid_ref(str, r0, st0), st0[r0 -- _type] .type ≤ ty, ∀ str, r, st, st0, r1, ty. validref(str, r, st[r -- _type] .type, st) ∧ st ⊆ st0 ∧ r ∈ acc ∧ validrefs(str, acc + r1 ', ty, st0) → validref(str, r1, st[r1 -- _type] .type, st) ⊦ r0 = jvmref, validref(str, r1, st[r1 -- _type] .type, st), r ≠ r0 ∧ ¬ r ∈ acc

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ is_obj(str, r, st) ∧ st[r -- _type] .type ≤ ty → ( validrefs(str, r ' + refs, ty, st) ↔ refs = [] ∨ (∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ refs .first = st[r -- fs '] .refval ∧ validrefs(str, refs, fs .type, st)))
Proof step 85:
¬ (is_obj(str, r0, st0) ∧ st0[r0 -- _type] .type ≤ ty), validref(str, r, st[r -- _type] .type, st), st ⊆ st0, validrefs(str, (r0 ' + acc) + r1 ', ty, st0), is_valid_ref(str, r0, st0), st0[r0 -- _type] .type ≤ ty, ∀ str, r, st, st0, r1, ty. validref(str, r, st[r -- _type] .type, st) ∧ st ⊆ st0 ∧ r ∈ acc ∧ validrefs(str, acc + r1 ', ty, st0) → validref(str, r1, st[r1 -- _type] .type, st) ⊦ r0 = jvmref, validref(str, r1, st[r1 -- _type] .type, st), r ≠ r0 ∧ ¬ r ∈ acc
Proof step 148:
is_obj(str, r0, st0) ∧ st0[r0 -- _type] .type ≤ ty, validref(str, r, st[r -- _type] .type, st), st ⊆ st0, acc + r1 ' = [] ∨ (∃ fs. fs ' ∈ instfields(st0[r0 -- _type] .type .class) ∧ is_referencevalue(st0[r0 -- fs ']) ∧ (acc + r1 ') .first = st0[r0 -- fs '] .refval ∧ validrefs(str, acc + r1 ', fs .type, st0)), is_valid_ref(str, r0, st0), st0[r0 -- _type] .type ≤ ty, ∀ str, r, st, st0, r1, ty. validref(str, r, st[r -- _type] .type, st) ∧ st ⊆ st0 ∧ r ∈ acc ∧ validrefs(str, acc + r1 ', ty, st0) → validref(str, r1, st[r1 -- _type] .type, st) ⊦ r0 = jvmref, validref(str, r1, st[r1 -- _type] .type, st), r ≠ r0 ∧ ¬ r ∈ acc

Rule argument

[crewrite-arg: validrefs-class , F , [st, ty, refs, r, str] → [st0, ty, acc + r1 ', r0, str] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])], [EXTRATERMS : (st0, ty, acc + r1 ', r0, str)]]