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Proof step 53 from proof validrefs-all-same (previous step)

st[r -- mkfs(class, ty1, fieldvar) '] = refval(r1), st0[r -- _type] .type = mkclasstype(class0), st[r -- _type] = st0[r -- _type], st0[r -- mkfs(class, ty1, fieldvar) '] = refval(r1), class0 ≤ class1, mkfs(class, ty1, fieldvar) ' ∈ instfields(class0), validrefs(str, r1 ' + refs, ty1, st), is_obj(str, r, st0), is_obj(str, r, st), validrefs(str, r1 ' + refs, ty1, st) ∧ (∀ r0. (r0 = r1 ∨ r0 ∈ refs) ∧ r0 ≠ jvmref → st[r0 -- _type] = st0[r0 -- _type] ∧ (is_classtype(st[r0 -- _type] .type) → (∀ sk. sk ∈ instfields(st[r0 -- _type] .type .class) → st[r0 -- sk] = st0[r0 -- sk])) ∧ ( is_arraytype(st[r0 -- _type] .type) → st[r0 -- _length] = st0[r0 -- _length] ∧ (∀ i. 0 ≤ i ∧ i < st[r0 -- _length] .intval → st[r0 -- i '] = st0[r0 -- i ']))) → validrefs(str, r1 ' + refs, ty1, st0), ∀ r0. (r0 = r ∨ r0 = r1 ∨ r0 ∈ refs) ∧ r0 ≠ jvmref → st[r0 -- _type] = st0[r0 -- _type] ∧ (is_classtype(st[r0 -- _type] .type) → (∀ sk. sk ∈ instfields(st[r0 -- _type] .type .class) → st[r0 -- sk] = st0[r0 -- sk])) ∧ ( is_arraytype(st[r0 -- _type] .type) → st[r0 -- _length] = st0[r0 -- _length] ∧ (∀ i. ¬ i < 0 ∧ ¬ st[r0 -- _length] .intval ≤ i → st[r0 -- i '] = st0[r0 -- i '])), ∀ sk. sk ∈ instfields(class0) → st[r -- sk] = st0[r -- sk] ⊦ r = jvmref, validrefs(str, r1 ' + refs, ty1, st0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 52:
st[r -- mkfs(class, ty1, fieldvar) '] = refval(r1), st0[r -- _type] .type = mkclasstype(class0), st[r -- _type] = st0[r -- _type], st0[r -- mkfs(class, ty1, fieldvar) '] = refval(r1), class0 ≤ class1, mkfs(class, ty1, fieldvar) ' ∈ instfields(class0), validrefs(str, r1 ' + refs, ty1, st), is_obj(str, r, st0), is_obj(str, r, st), ∀ r0. (r0 = r ∨ r0 = r1 ∨ r0 ∈ refs) ∧ r0 ≠ jvmref → st[r0 -- _type] = st0[r0 -- _type] ∧ (is_classtype(st[r0 -- _type] .type) → (∀ sk. sk ∈ instfields(st[r0 -- _type] .type .class) → st[r0 -- sk] = st0[r0 -- sk])) ∧ ( is_arraytype(st[r0 -- _type] .type) → st[r0 -- _length] = st0[r0 -- _length] ∧ (∀ i. ¬ i < 0 ∧ ¬ st[r0 -- _length] .intval ≤ i → st[r0 -- i '] = st0[r0 -- i '])), ∀ sk. sk ∈ instfields(class0) → st[r -- sk] = st0[r -- sk], r0 = r1 ∨ r0 ∈ refs ⊦ r = jvmref, r0 = jvmref, validrefs(str, r1 ' + refs, ty1, st0), st[r0 -- _type] = st0[r0 -- _type] ∧ (is_classtype(st[r0 -- _type] .type) → (sk ∈ instfields(st[r0 -- _type] .type .class) → st[r0 -- sk] = st0[r0 -- sk])) ∧ ( is_arraytype(st[r0 -- _type] .type) → st[r0 -- _length] = st0[r0 -- _length] ∧ (0 ≤ i ∧ i < st[r0 -- _length] .intval → st[r0 -- i '] = st0[r0 -- i ']))

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])]]