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Proof step 22 from proof validrefs-levelsubset-01 (previous step)

refs0 = r0 + refs, r0 = st[r -- mkfs(class, ty1, fieldvar) '] .refval, is_obj(str, r, st), is_obj(str0, r, st), level⊆(str, str0), validref(str, r, ty, st), st[r -- _type] .type ≤ ty0, st[r -- _type] .type ≤ ty, mkfs(class, ty1, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), is_referencevalue(st[r -- mkfs(class, ty1, fieldvar) ']), validrefs(str0, refs0, ty1, st), ∀ str, str0, ty0, st, ty. level⊆(str, str0) ∧ validrefs(str0, refs0, ty0, st) ∧ validref(str, r0, ty, st) → validrefs(str, refs0, ty0, st) ⊦ r = jvmref, refs0 = [], ∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ r0 = st[r -- fs '] .refval ∧ validrefs(str, refs0, fs .type, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 21:
is_obj(str, r, st), is_obj(str0, r, st), level⊆(str, str0), validref(str, r, ty, st), st[r -- _type] .type ≤ ty0, st[r -- _type] .type ≤ ty, mkfs(class, ty1, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), is_referencevalue(st[r -- mkfs(class, ty1, fieldvar) ']), validrefs(str0, st[r -- mkfs(class, ty1, fieldvar) '] .refval ' + refs, ty1, st), ∀ str1, str2, ty2, st0, ty3. level⊆(str1, str2) ∧ validrefs(str2, st[r -- mkfs(class, ty1, fieldvar) '] .refval ' + refs, ty2, st0) ∧ validref(str1, st[r -- mkfs(class, ty1, fieldvar) '] .refval, ty3, st0) → validrefs(str1, st[r -- mkfs(class, ty1, fieldvar) '] .refval ' + refs, ty2, st0) ⊦ r = jvmref, ∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ st[r -- mkfs(class, ty1, fieldvar) '] .refval = st[r -- fs '] .refval ∧ validrefs(str, st[r -- mkfs(class, ty1, fieldvar) '] .refval ' + refs, fs .type, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : list, references, a, ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPNAMEDSEQ : list, references, e-01, ⊦ r ' + refs ≠ []], [CSIMPNAMEDSEQ : list, references, c, ⊦ r + refs = r ' + refs])]]