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Proof step 25 from proof validrefs-put-statfield (previous step)

is_obj(str, r, st), st[r -- _type] .type ≤ ty, ∀ str, ty, st, sk, val. validrefs(str, acc, ty, st[jvmref -- sk, val]) ↔ validrefs(str, acc, ty, st) ⊦ r = jvmref, (∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ acc .first = st[r -- fs '] .refval ∧ validrefs(str, acc, fs .type, st[jvmref -- sk, val])) ↔ (∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ acc .first = st[r -- fs '] .refval ∧ validrefs(str, acc, fs .type, st)), acc = []

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 24:
acc = r0 + refs, is_obj(str, r, st), st[r -- _type] .type ≤ ty, ∀ str, ty, st, sk, val. validrefs(str, acc, ty, st[jvmref -- sk, val]) ↔ validrefs(str, acc, ty, st) ⊦ r = jvmref, (∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ r0 = st[r -- fs '] .refval ∧ validrefs(str, acc, fs .type, st[jvmref -- sk, val])) ↔ (∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ r0 = st[r -- fs '] .refval ∧ validrefs(str, acc, fs .type, st)), acc = []

Rule argument

[speclemmaarg: refs ≠ [] ,r = refs .first ∧ refs0 = refs .rest ↔ refs = r + refs0 ,[refs, r, refs0] → [acc, r0, refs] ,T ,list-data ,references-olista ,elim-list-c ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : refs ≠ [] ⊦ r = refs .first ∧ refs0 = refs .rest ↔ refs = r + refs0])], [EXTRATERMS : (acc, r0, refs)]]