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Proof step 14 from proof validrefs-levelsubset-01 (previous step)

st[r -- mkfs(class, ty1, fieldvar) '] = refval(r0), is_obj(str, r, st), is_obj(str0, r, st), level⊆(str, str0), st[r -- _type] .type ≤ ty0, st[r -- _type] .type ≤ ty, mkfs(class, ty1, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), validrefs(str0, r0 ' + refs, ty1, st), ∀ str1, str2, ty2, st0, ty3. level⊆(str1, str2) ∧ validrefs(str2, r0 ' + refs, ty2, st0) ∧ validref(str1, r0, ty3, st0) → validrefs(str1, r0 ' + refs, ty2, st0), ¬ mkfs(class, ty1, fieldvar) ' ∈ instfields(st[r -- _type] .type .class) ∨ ¬ is_referencevalue(st[r -- mkfs(class, ty1, fieldvar) ']) ∨ st[r -- mkfs(class, ty1, fieldvar) '] .refval = jvmref ∨ st[st[r -- mkfs(class, ty1, fieldvar) '] .refval -- _type] .type ≤ mkfs(class, ty1, fieldvar) .type ∧ validref(str, st[r -- mkfs(class, ty1, fieldvar) '] .refval, mkfs(class, ty1, fieldvar) .type, st) ⊦ r = jvmref, validrefs(str, r0 ' + refs, ty1, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
⊦ validrefs(str, jvmref ' + refs, ty, st) ↔ refs = []
Proof step 13:
st[r -- mkfs(class, ty1, fieldvar) '] = refval(r0), validrefs(str0, r0 ' + refs, ty1, st), mkfs(class, ty1, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), st[r -- _type] .type ≤ ty, st[r -- _type] .type ≤ ty0, level⊆(str, str0), is_obj(str0, r, st), is_obj(str, r, st), st[r0 -- _type] .type ≤ ty1, validref(str, r0, ty1, st), ∀ str1, str2, ty2, st0, ty3. level⊆(str1, str2) ∧ validrefs(str2, r0 ' + refs, ty2, st0) ∧ validref(str1, r0, ty3, st0) → validrefs(str1, r0 ' + refs, ty2, st0) ⊦ r = jvmref, r0 = jvmref, validrefs(str, r0 ' + refs, ty1, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : list, references, a, ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPNAMEDSEQ : javavalue, , sel-09, ⊦ refval(r) .refval = r], [CSIMPNAMEDSEQ : javavalue, , test-19, ⊦ is_referencevalue(refval(r))], [CSIMPNAMEDSEQ : fieldspec, , sel-03, ⊦ mkfs(class, ty, fieldvar) .type = ty])]]