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Proof step 53 from proof junkrefs-put-nopathexplus-equiv (previous step)

st[r -- mkfs(class, ty0, fieldvar) '] = refval(r1), st[r -- _type] .type ≤ ty, is_obj(str, r, st), mkfs(class, ty0, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), junkrefs(str, r1 ' + refs1, ty0, st), ∀ val, sk, r0, st0, ty, r2, str, refs. # refs < # (r1 + refs1) → (junkrefs(str, r2 ' + refs, ty, st0) → junkrefs(str, r2 ' + refs, ty, st0[r0 -- sk, val]) ∨ sk = _type ∨ path∃+(str, r2, r0, st0)) ⊦ sk = _type, r = jvmref, r = r0, path∃+(str, r, r0, st), junkrefs(str, r1 ' + refs1, ty0, st[r0 -- sk, val])

User applied rule apply induction

And obtained the following new goals

Proof step 52:
junkrefs(str, r1 ' + refs1, ty0, st[r0 -- sk, val]) ∨ sk = _type ∨ path∃+(str, r1, r0, st), st[r -- mkfs(class, ty0, fieldvar) '] = refval(r1), st[r -- _type] .type ≤ ty, is_obj(str, r, st), mkfs(class, ty0, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), junkrefs(str, r1 ' + refs1, ty0, st), ∀ val, sk, r0, st0, ty, r2, str, refs. # refs < # (r1 + refs1) → (junkrefs(str, r2 ' + refs, ty, st0) → junkrefs(str, r2 ' + refs, ty, st0[r0 -- sk, val]) ∨ sk = _type ∨ path∃+(str, r2, r0, st0)) ⊦ sk = _type, r = jvmref, r = r0, path∃+(str, r, r0, st), junkrefs(str, r1 ' + refs1, ty0, st[r0 -- sk, val])

Rule argument

[substlist-arg: [val, sk, r0, st0, ty, r2, str, refs] → [val, sk, r0, st, ty0, r1, str, refs1] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r + refs = r ' + refs], [CSIMPSEQ : ⊦ # (refs + refs0) = # refs + # refs0], [CSIMPSEQ : ⊦ # r ' = 0 +1], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ m < n + 1 ↔ ¬ n < m], [CSIMPSEQ : ⊦ ¬ n < n], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ m + n = n + m])], [EXTRATERMS : (val, sk, r0, st, ty0, r1, str, refs1)]]