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Proof step 42 from proof validrefs-trans-01 (previous step)

is_obj(str, r, st) ∧ st[r -- _type] .type ≤ ty, st[r -- mkfs(class, ty3, fieldvar) '] = refval(r0), is_obj(str, r, st), validrefs(str, r0 ', ty3, st), mkfs(class, ty3, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), st[r -- _type] .type ≤ ty, validrefs(str, r0 ' + refs1, ty0, st), ∀ str0, ty1, st0, refs, ty2. validrefs(str0, r0 ', ty1, st0) ∧ validrefs(str0, r0 ' + refs, ty2, st0) → validrefs(str0, r0 ' + refs, ty1, st0) ⊦ r = jvmref, r0 ' + refs1 = [] ∨ (∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ (r0 ' + refs1) .first = st[r -- fs '] .refval ∧ validrefs(str, r0 ' + refs1, fs .type, st))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 41:
st[r -- mkfs(class, ty3, fieldvar) '] = refval(r0), is_obj(str, r, st), validrefs(str, r0 ', ty3, st), mkfs(class, ty3, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), st[r -- _type] .type ≤ ty, validrefs(str, r0 ' + refs1, ty0, st), ∀ str0, ty1, st0, refs, ty2. validrefs(str0, r0 ', ty1, st0) ∧ validrefs(str0, r0 ' + refs, ty2, st0) → validrefs(str0, r0 ' + refs, ty1, st0) ⊦ r = jvmref, ∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ r0 = st[r -- fs '] .refval ∧ validrefs(str, st[r -- fs '] .refval ' + refs1, fs .type, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (r ' + refs) .first = r], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ r ' + refs ≠ []])]]