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Proof step 71 from proof validrefs-putbyte-field (previous step)

(st[r -- mkfs(class, byte_type, fieldvar) ', byteval(by)][r0 -- mkfs(class0, ty0, fieldvar0) ']) = refval(r1), validrefs(str, r1 ' + refs, ty0, st[r -- mkfs(class, byte_type, fieldvar) ', byteval(by)]), mkfs(class0, ty0, fieldvar0) ' ∈ instfields(st[r0 -- _type] .type .class), st[r0 -- _type] .type ≤ ty, is_obj(str, r0, st[r -- mkfs(class, byte_type, fieldvar) ', byteval(by)]), ∀ by0, fieldvar1, class1, r2, st0, ty, str, refs0. # refs0 < # (r0 + r1 + refs) → ( validrefs(str, refs0, ty, st0[r2 -- mkfs(class1, byte_type, fieldvar1) ', byteval(by0)]) → refs0 = [] ∨ junkref(str, refs0 .first, st0) ∨ validrefs(str, refs0, ty, st0)) ⊦ r0 = jvmref, validrefs(str, r0 ' + r1 ' + refs, ty, st), junkref(str, r0, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 47:
⊦ rk ≠ rk0 → (st[rk0, val][rk]) = st[rk]
Proof step 70:
r0 -- mkfs(class0, ty0, fieldvar0) ' ≠ r -- mkfs(class, byte_type, fieldvar) ', st[r0 -- mkfs(class0, ty0, fieldvar0) '] = refval(r1), validrefs(str, r1 ' + refs, ty0, st[r -- mkfs(class, byte_type, fieldvar) ', byteval(by)]), mkfs(class0, ty0, fieldvar0) ' ∈ instfields(st[r0 -- _type] .type .class), st[r0 -- _type] .type ≤ ty, is_obj(str, r0, st[r -- mkfs(class, byte_type, fieldvar) ', byteval(by)]), ∀ by0, fieldvar1, class1, r2, st0, ty, str, refs0. # refs0 < # (r0 + r1 + refs) → ( validrefs(str, refs0, ty, st0[r2 -- mkfs(class1, byte_type, fieldvar1) ', byteval(by0)]) → refs0 = [] ∨ junkref(str, refs0 .first, st0) ∨ validrefs(str, refs0, ty, st0)) ⊦ r0 = jvmref, validrefs(str, r0 ' + r1 ' + refs, ty, st), junkref(str, r0, st)

Rule argument

[speclemmaarg: ,rk ≠ rk0 → (st[rk0, val][rk]) = st[rk] ,[rk, val, rk0, st] → [r0 -- mkfs(class0, ty0, fieldvar0) ', byteval(by), r -- mkfs(class, byte_type, fieldvar) ', st] ,F ,store ,javastore-ostorea ,At-other ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ r = r0 ∧ sk = sk0], [CSIMPSEQ : ⊦ fs ' = fs0 ' ↔ fs = fs0], [CSIMPSEQ : ⊦ mkfs(class, ty, fieldvar) = mkfs(class0, ty0, fieldvar0) ↔ class = class0 ∧ ty = ty0 ∧ fieldvar = fieldvar0], [CSIMPSEQ : ⊦ (st[rk, val][rk]) = val], [CSIMPSEQ : ⊦ byteval(by) ≠ refval(r)])], [EXTRATERMS : (r0 -- mkfs(class0, ty0, fieldvar0) ', byteval(by), r -- mkfs(class, byte_type, fieldvar) ', st)]]