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Proof step 39 from proof pathex-put-nopathex (previous step)

st[r -- mkfs(class, ty, fieldvar) '] = refval(r1), validrefs(str, r1 ' + refs1, ty, st[r0 -- sk, val]), mkfs(class, ty, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), is_obj(str, r, st), ∀ val0, sk0, r3, st0, r2, str, refs. # refs < # (r1 + refs1) → ( validrefs(str, r2 ' + refs, st0[r2 -- _type] .type, st0[r3 -- sk0, val0]) → sk0 = _type ∨ path∃(str, r2, r3, st0) ∨ junkref(str, r2, st0) ∨ path∃(str, r2, (r2 ' + refs) .last, st0)) ⊦ r = jvmref, sk = _type, r = r0, path∃(str, r, (r1 ' + refs1) .last, st), path∃(str, r, r0, st), junkref(str, r, st)

User applied rule apply induction

And obtained the following new goals

Proof step 12:
st[r -- mkfs(class, ty, fieldvar) '] = refval(r1), validrefs(str, r1 ' + refs1, ty, st[r0 -- sk, val]), mkfs(class, ty, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), is_obj(str, r, st), ∀ val0, sk0, r3, st0, r2, str, refs. # refs < # (r1 + refs1) → ( validrefs(str, r2 ' + refs, st0[r2 -- _type] .type, st0[r3 -- sk0, val0]) → sk0 = _type ∨ path∃(str, r2, r3, st0) ∨ junkref(str, r2, st0) ∨ path∃(str, r2, (r2 ' + refs) .last, st0)) ⊦ validrefs(str, r1 ' + refs1, st[r1 -- _type] .type, st[r0 -- sk, val]), r = jvmref, sk = _type, r = r0, path∃(str, r, (r1 ' + refs1) .last, st), path∃(str, r, r0, st), junkref(str, r, st)
Proof step 38:
sk = _type ∨ path∃(str, r1, r0, st) ∨ junkref(str, r1, st) ∨ path∃(str, r1, (r1 ' + refs1) .last, st), st[r -- mkfs(class, ty, fieldvar) '] = refval(r1), validrefs(str, r1 ' + refs1, ty, st[r0 -- sk, val]), mkfs(class, ty, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), is_obj(str, r, st), ∀ val0, sk0, r3, st0, r2, str, refs. # refs < # (r1 + refs1) → ( validrefs(str, r2 ' + refs, st0[r2 -- _type] .type, st0[r3 -- sk0, val0]) → sk0 = _type ∨ path∃(str, r2, r3, st0) ∨ junkref(str, r2, st0) ∨ path∃(str, r2, (r2 ' + refs) .last, st0)) ⊦ r = jvmref, sk = _type, r = r0, path∃(str, r, (r1 ' + refs1) .last, st), path∃(str, r, r0, st), junkref(str, r, st)

Rule argument

[substlist-arg: [val0, sk0, r3, st0, r2, str, refs] → [val, sk, r0, st, 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, r1, str, refs1)]]