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Proof step 124 from proof exvalidrefs-nodups (previous step)

st[r -- mkfs(class0, ty, fieldvar) '] = refval(jvmref), st[r -- _type] .type ≤ mkclasstype(class), st[r -- _type] .type ≤ ty, ty ≤ mkclasstype(class), mkfs(class0, ty, fieldvar) ' ∈ instfields(class), is_obj(str, r, st), is_classtype(st[r -- _type] .type), ∀ r, str, st0. # st0 .refs < # st .refs → ( ¬ junkref(str, r, st0) ∧ ¬ cyclic(str, r, st0) ∧ is_obj(str, r, st0) ∧ r ≠ jvmref ∧ (∃ fs, class. fs ' ∈ instfields(class) ∧ fs .type ≤ mkclasstype(class) ∧ st0[r -- _type] .type ≤ fs .type) → (∃ refs. validrefs(str, refs, st0[r -- _type] .type, st0) ∧ refs ≠ [] ∧ ¬ dups(refs) ∧ refs .first = r ∧ refs .last = jvmref)) ⊦ r = jvmref, cyclic(str, r, st), validrefs(str, r ' + jvmref ', st[(r ' + jvmref ') .first -- _type] .type, st) ∧ r ' + jvmref ' ≠ [] ∧ ¬ dups(r ' + jvmref ') ∧ (r ' + jvmref ') .first = r ∧ (r ' + jvmref ') .last = jvmref

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 123:
st[r -- mkfs(class0, ty, fieldvar) '] = refval(jvmref), st[r -- _type] .type ≤ mkclasstype(class), st[r -- _type] .type ≤ ty, ty ≤ mkclasstype(class), mkfs(class0, ty, fieldvar) ' ∈ instfields(class), is_obj(str, r, st), is_classtype(st[r -- _type] .type), ∀ r, str, st0. # st0 .refs < # st .refs → ( ¬ junkref(str, r, st0) ∧ ¬ cyclic(str, r, st0) ∧ is_obj(str, r, st0) ∧ r ≠ jvmref ∧ (∃ fs, class. fs ' ∈ instfields(class) ∧ fs .type ≤ mkclasstype(class) ∧ st0[r -- _type] .type ≤ fs .type) → (∃ refs. validrefs(str, refs, st0[r -- _type] .type, st0) ∧ refs ≠ [] ∧ ¬ dups(refs) ∧ refs .first = r ∧ refs .last = jvmref)) ⊦ r = jvmref, cyclic(str, r, st), validrefs(str, r ' + jvmref ', st[r -- _type] .type, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (refs + r ') .last = r], [CSIMPSEQ : ⊦ ¬ dups(r ')], [CSIMPSEQ : ⊦ r ∈ r0 ' ↔ r = r0], [CSIMPSEQ : ⊦ dups(r ' + refs) ↔ ¬ ¬ (r ∈ refs ∨ dups(refs))], [CSIMPSEQ : ⊦ r ' ≠ []], [CSIMPSEQ : ⊦ ¬ refs + refs0 ≠ [] ↔ refs = [] ∧ refs0 = []], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ (r ' + refs) .first = r])]]