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Proof step 56 from proof junkrefs-put-refval (previous step)

(st[r1 -- mkfs(class, ty0, fieldvar) ', refval(r0)][r1 -- mkfs(class0, ty2, fieldvar0) ']) = refval(r3), junkrefs(str, r3 ' + refs, ty2, st[r1 -- mkfs(class, ty0, fieldvar) ', refval(r0)]), is_valid_ref(str, r1, st), st[r1 -- _type] .type ≤ ty, is_obj(str, r1, st[r1 -- mkfs(class, ty0, fieldvar) ', refval(r0)]), (st[r1 -- mkfs(class, ty0, fieldvar) ', refval(r0)][r1 -- _type]) .type ≤ ty, is_obj(r1, st), st[r0 -- _type] .type ≤ ty0, mkfs(class, ty0, fieldvar) ' ∈ instfields(st[r1 -- _type] .type .class), mkfs(class0, ty2, fieldvar0) ' ∈ instfields((st[r1 -- mkfs(class, ty0, fieldvar) ', refval(r0)][r1 -- _type]) .type .class), ∀ str0, ty1, st0, r, r2, fs0. ¬ junkrefs(str0, r3 ' + refs, ty1, st0) ∧ ¬ junkref(str0, r, st0) ∧ is_obj(r2, st0) ∧ st0[r -- _type] .type ≤ fs0 .type ∧ r ≠ jvmref ∧ fs0 ' ∈ instfields(st0[r2 -- _type] .type .class) → ¬ junkrefs(str0, r3 ' + refs, ty1, st0[r2 -- fs0 ', refval(r)]) ⊦ r1 = jvmref, r0 = jvmref, junkrefs(str, r1 ' + r3 ' + refs, ty, st), junkref(str, r0, st)

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Proof step 55:
(st[r1 -- mkfs(class, ty0, fieldvar) ', refval(r0)][r1 -- mkfs(class0, ty2, fieldvar0) ']) = refval(r3), junkrefs(str, r3 ' + refs, ty2, st[r1 -- mkfs(class, ty0, fieldvar) ', refval(r0)]), is_valid_ref(str, r1, st), st[r1 -- _type] .type ≤ ty, is_obj(str, r1, st[r1 -- mkfs(class, ty0, fieldvar) ', refval(r0)]), (st[r1 -- mkfs(class, ty0, fieldvar) ', refval(r0)][r1 -- _type]) .type ≤ ty, is_obj(r1, st), st[r0 -- _type] .type ≤ ty0, mkfs(class, ty0, fieldvar) ' ∈ instfields(st[r1 -- _type] .type .class), mkfs(class0, ty2, fieldvar0) ' ∈ instfields((st[r1 -- mkfs(class, ty0, fieldvar) ', refval(r0)][r1 -- _type]) .type .class), ∀ str0, ty1, st0, r, r2, fs0. ¬ junkrefs(str0, r3 ' + refs, ty1, st0) ∧ ¬ junkref(str0, r, st0) ∧ is_obj(r2, st0) ∧ st0[r -- _type] .type ≤ fs0 .type ∧ r ≠ jvmref ∧ fs0 ' ∈ instfields(st0[r2 -- _type] .type .class) → ¬ junkrefs(str0, r3 ' + refs, ty1, st0[r2 -- fs0 ', refval(r)]) ⊦ r1 -- _type = r1 -- mkfs(class, ty0, fieldvar) ', r1 = jvmref, r0 = jvmref, junkrefs(str, r1 ' + r3 ' + refs, ty, st), junkref(str, r0, st)

Rule argument

[fma-arg: r1 -- _type = r1 -- mkfs(class, ty0, fieldvar) ']

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ r = r0 ∧ sk = sk0], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [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 : ⊦ (st[rk, val][rk]) = val], [CSIMPSEQ : ⊦ ¬ _type ∈ instfields(class)])], [EXTRAFMAS : (r1 -- _type = r1 -- mkfs(class, ty0, fieldvar) ')]]