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Proof step 121 from proof pathex-put-nopathex (previous step)

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

User applied rule cut formula

And obtained the following new goals

Proof step 116:
⊦ validrefs(str, jvmref ' + refs, ty, st) ↔ refs = []
Proof step 117:
⊦ r ≠ jvmref → ¬ path∃(str, jvmref, r, st)
Proof step 120:
st[r -- mkfs(class, ty, fieldvar) '] = refval(r1), is_obj(str, r, st), validrefs(str, r1 ' + refs1, ty, st), mkfs(class, ty, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), path∃(str, r1, r0, st) ∨ junkref(str, r1, st) ∨ path∃(str, r1, (r1 ' + refs1) .last, st[r0 -- sk, val]), ∀ val, r0, sk, st0, r2, str, refs. # refs < # (r1 + refs1) → ( validrefs(str, r2 ' + refs, st0[r2 -- _type] .type, st0) → sk = _type ∨ path∃(str, r2, r0, st0) ∨ junkref(str, r2, st0) ∨ path∃(str, r2, (r2 ' + refs) .last, st0[r0 -- sk, val])) ⊦ r1 = jvmref, r = (r1 ' + refs1) .last, r = r0, r = jvmref, sk = _type, r1 = jvmref ∧ r0 = jvmref, r1 ≠ jvmref ∧ st[r1 -- _type] .type ≤ ty ∧ path∃(str, r1, r0, st), (is_reftype(ty) ∨ ty = abstract_type) ∧ r1 ≠ jvmref ∧ (¬ st[r1 -- _type] .type ≤ ty ∨ junkref(str, r1, st)), r1 ≠ jvmref ∧ st[r1 -- _type] .type ≤ ty ∧ path∃(str, r1, (r1 ' + refs1) .last, st[r0 -- sk, val]), r1 = jvmref ∧ (jvmref ' + refs1) .last = jvmref

Rule argument

[fma-arg: r1 = jvmref]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ ¬ junkref(str, jvmref, st)])], [EXTRAFMAS : (r1 = jvmref)]]