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Proof step 21 from proof put-switch-primval-field-field (previous step)

st[r -- sks1] = refval(r1), fits(r2, mkfs(class0, ty0, fieldvar0) ' ', st), fits(r, sks1 + mkfs(class, ty, fieldvar) ' ', st), r1 ≠ r2 ∨ class ≠ class0 ∨ ty ≠ ty0 ∨ fieldvar ≠ fieldvar0 ⊦ (st[r1 -- mkfs(class, ty, fieldvar) ', val][r2 -- mkfs(class0, ty0, fieldvar0) ', val0]) = (st[r2 -- mkfs(class0, ty0, fieldvar0) ', val0] [(st[r2 -- mkfs(class0, ty0, fieldvar0) ', val0][r -- sks1]) .refval -- mkfs(class, ty, fieldvar) ', val ] ), junkref(str, r2, st), junkref(str, r, st), is_reftype(ty0), is_reftype(ty), is_referencevalue(val0), is_referencevalue(val)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
⊦ rk ≠ rk0 → (st[rk0, val][rk, val0]) = (st[rk, val0][rk0, val])
Proof step 20:
r2 -- mkfs(class0, ty0, fieldvar0) ' ≠ r1 -- mkfs(class, ty, fieldvar) ', st[r -- sks1] = refval(r1), fits(r2, mkfs(class0, ty0, fieldvar0) ' ', st), fits(r, sks1 + mkfs(class, ty, fieldvar) ' ', st), r1 ≠ r2 ∨ class ≠ class0 ∨ ty ≠ ty0 ∨ fieldvar ≠ fieldvar0 ⊦ (st[r2 -- mkfs(class0, ty0, fieldvar0) ', val0][r1 -- mkfs(class, ty, fieldvar) ', val]) = (st[r2 -- mkfs(class0, ty0, fieldvar0) ', val0] [(st[r2 -- mkfs(class0, ty0, fieldvar0) ', val0][r -- sks1]) .refval -- mkfs(class, ty, fieldvar) ', val ] ), junkref(str, r2, st), junkref(str, r, st), is_reftype(ty0), is_reftype(ty), is_referencevalue(val0), is_referencevalue(val)

Rule argument

[x0lemmaarg: spec-name: store instance-name: javastore lemma-name: rew antecedent: succedent: rk ≠ rk0 → (st[rk0, val][rk, val0]) = (st[rk, val0][rk0, val]) substlist: [val0, rk, val, rk0, st] → [val0, r2 -- mkfs(class0, ty0, fieldvar0) ', val, r1 -- mkfs(class, ty, fieldvar) ', st] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((1, 0, 0, 1, 0)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : refkey, , inj, ⊦ r -- sk = r0 -- sk0 ↔ r = r0 ∧ sk = sk0], [CSIMPNAMEDSEQ : storekey, , inj-03, ⊦ fs ' = fs0 ' ↔ fs = fs0], [CSIMPNAMEDSEQ : fieldspec, , inj, ⊦ mkfs(class, ty, fieldvar) = mkfs (class0, ty0, fieldvar0) ↔ class = class0 ∧ ty = ty0 ∧ fieldvar = fieldvar0])], [EXTRATERMS : (val0, r2 -- mkfs(class0, ty0, fieldvar0) ', val, r1 -- mkfs(class, ty, fieldvar) ', st)]]