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Proof step 52 from proof pathex-put-cyclic (previous step)

st[r0 -- _type] .type = mkclasstype(class0), mkfs(class, ty, fieldvar) ' ∈ instfields(class0), st[r -- _type] .type ≤ ty, validrefs(str, r ' + refs0 + r0 ', st[r -- _type] .type, st) ⊦ r = jvmref, r0 = jvmref, r = r0, r0 ∈ refs0, dups(refs0), r ∈ refs0, validrefs (str, r0 ' + r ' + refs0 + r0 ', (st[r0 -- mkfs(class, ty, fieldvar) ', refval(r)][r0 -- _type]) .type, st[r0 -- mkfs(class, ty, fieldvar) ', refval(r)]), ∃ refs. dups(refs) ∧ refs .first = r0 ∧ validrefs (str, refs, (st[refs .first -- mkfs(class, ty, fieldvar) ', refval(r)][refs .first -- _type]) .type, st[refs .first -- mkfs(class, ty, fieldvar) ', refval(r)])

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Proof step 51:
st[r0 -- _type] .type = mkclasstype(class0), mkfs(class, ty, fieldvar) ' ∈ instfields(class0), st[r -- _type] .type ≤ ty, validrefs(str, r ' + refs0 + r0 ', st[r -- _type] .type, st) ⊦ r0 -- _type = r0 -- mkfs(class, ty, fieldvar) ', r = jvmref, r0 = jvmref, r = r0, r0 ∈ refs0, dups(refs0), r ∈ refs0, validrefs (str, r0 ' + r ' + refs0 + r0 ', (st[r0 -- mkfs(class, ty, fieldvar) ', refval(r)][r0 -- _type]) .type, st[r0 -- mkfs(class, ty, fieldvar) ', refval(r)]), ∃ refs. dups(refs) ∧ refs .first = r0 ∧ validrefs (str, refs, (st[refs .first -- mkfs(class, ty, fieldvar) ', refval(r)][refs .first -- _type]) .type, st[refs .first -- mkfs(class, ty, fieldvar) ', refval(r)])

Rule argument

[fma-arg: r0 -- _type = r0 -- mkfs(class, ty, fieldvar) ']

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ r = r0 ∧ sk = sk0], [CSIMPFORWARD : ⊦ _type = mkfs(class1, ty, fieldvar) ' → class1 = `java.lang.Object' .class ∧ ty = void_type ∧ fieldvar = `type' .field], [CSIMPSEQ : ⊦ mkfs (`java.lang.Object' .class, void_type, `type' .field) ' = _type], [CSIMPSEQ : ⊦ ty ≤ void_type ↔ ty = void_type], [CSIMPSEQ : ⊦ ¬ _type ∈ instfields(class)])], [EXTRAFMAS : (r0 -- _type = r0 -- mkfs(class, ty, fieldvar) ')]]