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Proof step 18 from proof validrefs-maxlen (previous step)

acc = r0 + refs, r0 = st[r -- fs '] .refval, is_obj(str, r, st), # st .refs < # acc, st[r -- _type] .type ≤ ty, fs ' ∈ instfields(st[r -- _type] .type .class), is_referencevalue(st[r -- fs ']), validrefs(str, acc, fs .type, st), ∀ str0, ty0, st0. validrefs(str0, acc, ty0, st0) → # acc ≤ # st0 .refs + 1 ⊦ r = jvmref, acc = [], dups(acc), r ∈ acc

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 17:
is_obj(str, r, st), # st .refs ≤ # refs, st[r -- _type] .type ≤ ty, fs ' ∈ instfields(st[r -- _type] .type .class), is_referencevalue(st[r -- fs ']), validrefs(str, st[r -- fs '] .refval ' + refs, fs .type, st), ∀ str0, ty0, st0. validrefs(str0, st[r -- fs '] .refval ' + refs, ty0, st0) → # refs ≤ # st0 .refs ⊦ r = jvmref, r = st[r -- fs '] .refval, dups(refs), st[r -- fs '] .refval ∈ refs, r ∈ refs

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ m + n ≤ m + n0 ↔ n ≤ n0], [CSIMPSEQ : ⊦ ¬ r ∈ r0 ' + refs ↔ r ≠ r0 ∧ ¬ r ∈ refs], [CSIMPSEQ : ⊦ dups(r ' + refs) ↔ dups(refs) ∨ r ∈ refs], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ ¬ m < n ↔ n ≤ m], [CSIMPSEQ : ⊦ m < n + 1 ↔ ¬ n < m], [CSIMPSEQ : ⊦ # r ' = 0 +1], [CSIMPSEQ : ⊦ # (refs + refs0) = # refs + # refs0], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ r ' + refs ≠ []], [CSIMPSEQ : ⊦ r + refs = r ' + refs])]]