Proof step 1 from proof event-persistDependentReads (conclusion) (back to tree)

System applied rule normalize

And obtained the following new goals

• Proof step 2:

  events(persistDependentReads(l, h)) ≠ events(h) ⊦

Rule argument

Additional information

Proof step 2 from proof event-persistDependentReads (previous step) (back to tree)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

• Proof step 3:

  persistDependentReads(l, h).map(._1) ≠ h.map(._1) ⊦

Rule argument

Additional information

Used simplifier rules: restrict-events: ⊦ events(h) = h.map(λ vpe. vpe._1);

Proof step 3 from proof event-persistDependentReads (previous step) (back to tree)

Heuristic structural induction applied rule structural induction

And obtained the following new goals

• Proof step 4:

  persistDependentReads(l, vpe + h0).map(._1) ≠ (vpe + h0).map(._1), ∀ l. persistDependentReads(l, h0).map(._1) = h0.map(._1) ⊦

Rule argument

Additional information

Used simplifier rules: persistDependentReads-base: ⊦ persistDependentReads(l, []) = []; List('a) freely generated by [], +;; ⊦ [].map(f) = []; (s)

Proof step 4 from proof event-persistDependentReads (previous step) (back to tree)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

• Proof step 5:

  persistDependentReads(l, vpe ' + h0).map(._1) ≠ vpe._1 ' + h0.map(._1), ∀ l. persistDependentReads(l, h0).map(._1) = h0.map(._1) ⊦

Rule argument

Additional information

Used simplifier rules: a: ⊦ (x + y) + z = x + y + z; from specification list ⊦ a + x = a ' + x; (s) ⊦ (a ' + x).map(f) = f(a) + x.map(f); (s)

Proof step 5 from proof event-persistDependentReads (previous step) (back to tree)

Heuristic elimination applied rule apply elim lemma

And obtained the following new goals

• Proof step 6:

  vpe = (e, boolvar), persistDependentReads(l, vpe ' + h0).map(._1) ≠ e ' + h0.map(._1), ∀ l. persistDependentReads(l, h0).map(._1) = h0.map(._1) ⊦

Rule argument

Additional information

Used terms: e, boolvar

Proof step 6 from proof event-persistDependentReads (previous step) (back to tree)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

• Proof step 7:

  persistDependentReads(l, (e, boolvar) ' + h0).map(._1) ≠ e ' + h0.map(._1), ∀ l. persistDependentReads(l, h0).map(._1) = h0.map(._1) ⊦

Rule argument

Additional information

Proof step 7 from proof event-persistDependentReads (previous step) (back to tree)

User applied rule constructor cut

And obtained the following new goals

• Proof step 8:

  e = R(t, l0, v), persistDependentReads(l, (e, boolvar) ' + h0).map(._1) ≠ e ' + h0.map(._1), ∀ l. persistDependentReads(l, h0).map(._1) = h0.map(._1) ⊦

• Proof step 24:

  e = W(t, l0, v), persistDependentReads(l, (e, boolvar) ' + h0).map(._1) ≠ e ' + h0.map(._1), ∀ l. persistDependentReads(l, h0).map(._1) = h0.map(._1) ⊦

Rule argument

Additional information

Used simplifier rules: RWevent freely generated by R, W;;

Proof step 8 from proof event-persistDependentReads (previous step) (back to tree)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

• Proof step 9:

  persistDependentReads(l, (R(t, l0, v), boolvar) ' + h0).map(._1) ≠ R(t, l0, v) ' + h0.map(._1), ∀ l. persistDependentReads(l, h0).map(._1) = h0.map(._1) ⊦

Rule argument

Additional information

Proof step 9 from proof event-persistDependentReads (previous step) (back to tree)

User applied rule cut formula

And obtained the following new goals

• Proof step 10:

  boolvar, persistDependentReads(l, (R(t, l0, v), boolvar) ' + h0).map(._1) ≠ R(t, l0, v) ' + h0.map(._1), ∀ l. persistDependentReads(l, h0).map(._1) = h0.map(._1) ⊦

• Proof step 17:

  ¬ boolvar, persistDependentReads(l, (R(t, l0, v), boolvar) ' + h0).map(._1) ≠ R(t, l0, v) ' + h0.map(._1), ∀ l. persistDependentReads(l, h0).map(._1) = h0.map(._1) ⊦

Rule argument

Additional information

Used formulas: boolvar

Proof step 10 from proof event-persistDependentReads (previous step) (back to tree)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

• Proof step 11:

  persistDependentReads(l, (R(t, l0, v), true) ' + h0).map(._1) ≠ R(t, l0, v) ' + h0.map(._1), ∀ l. persistDependentReads(l, h0).map(._1) = h0.map(._1) ⊦

Rule argument

Additional information

Proof step 11 from proof event-persistDependentReads (previous step) (back to tree)

User applied rule apply rewrite lemma

And obtained the following new goals

• Proof step 12:

  ⊦ l ≠ l0 → persistDependentReads(l, (R(t, l0, v), b) ' + h) = (R(t, l0, v), b) + persistDependentReads(l, h)

• Proof step 13:

  l = l0, persistDependentReads(l, (R(t, l0, v), true) ' + h0).map(._1) ≠ R(t, l0, v) ' + h0.map(._1), ∀ l. persistDependentReads(l, h0).map(._1) = h0.map(._1) ⊦

• Proof step 15:

  ((R(t, l0, v), true) + persistDependentReads(l, h0)).map(._1) ≠ R(t, l0, v) ' + h0.map(._1), l ≠ l0, ∀ l. persistDependentReads(l, h0).map(._1) = h0.map(._1) ⊦

Rule argument

Additional information

Used simplifier rules: a: ⊦ (x + y) + z = x + y + z; from specification list Used terms: v, true, l, l0, t, h0

Proof step 12 from proof event-persistDependentReads (previous step) (back to tree)

Lemma persistDependentReads-otherread

Proof step 13 from proof event-persistDependentReads (previous step) (back to tree)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

• Proof step 14:

  persistDependentReads(l0, h0).map(._1) ≠ h0.map(._1), ∀ l. persistDependentReads(l, h0).map(._1) = h0.map(._1) ⊦

Rule argument

Additional information

Used simplifier rules: persistDependentReads-read: ⊦ persistDependentReads(l, (R(t, l, v), b) ' + h) = (R(t, l, v), true) ' + persistDependentReads(l, h); a: ⊦ (x + y) + z = x + y + z; from specification list ⊦ # x = # z → (x + y = z + y0 ↔ x = z ∧ y = y0); (ws) ⊦ a + x = a ' + x; (s) ⊦ (a ' + x).map(f) = f(a) + x.map(f); (s)

Proof step 14 from proof event-persistDependentReads (previous step) (back to tree)

Heuristic quantifier closing applied rule all left

And closed the goal!

Rule argument

Additional information

Used terms: l0

Proof step 15 from proof event-persistDependentReads (previous step) (back to tree)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

• Proof step 16:

  persistDependentReads(l, h0).map(._1) ≠ h0.map(._1), l ≠ l0, ∀ l. persistDependentReads(l, h0).map(._1) = h0.map(._1) ⊦

Rule argument

Additional information

Used simplifier rules: a: ⊦ (x + y) + z = x + y + z; from specification list ⊦ # x = # z → (x + y = z + y0 ↔ x = z ∧ y = y0); (ws) ⊦ a + x = a ' + x; (s) ⊦ (a ' + x).map(f) = f(a) + x.map(f); (s)

Proof step 16 from proof event-persistDependentReads (previous step) (back to tree)

Heuristic quantifier closing applied rule all left

And closed the goal!

Rule argument

Additional information

Used terms: l

Proof step 17 from proof event-persistDependentReads (previous step) (back to tree)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

• Proof step 18:

  persistDependentReads(l, (R(t, l0, v), false) ' + h0).map(._1) ≠ R(t, l0, v) ' + h0.map(._1), ∀ l. persistDependentReads(l, h0).map(._1) = h0.map(._1) ⊦

Rule argument

Additional information

Proof step 18 from proof event-persistDependentReads (previous step) (back to tree)

User applied rule apply rewrite lemma

And obtained the following new goals

• Proof step 19:

  ⊦ l ≠ l0 → persistDependentReads(l, (R(t, l0, v), b) ' + h) = (R(t, l0, v), b) + persistDependentReads(l, h)

• Proof step 20:

  l = l0, persistDependentReads(l, (R(t, l0, v), false) ' + h0).map(._1) ≠ R(t, l0, v) ' + h0.map(._1), ∀ l. persistDependentReads(l, h0).map(._1) = h0.map(._1) ⊦

• Proof step 22:

  ((R(t, l0, v), false) + persistDependentReads(l, h0)).map(._1) ≠ R(t, l0, v) ' + h0.map(._1), l ≠ l0, ∀ l. persistDependentReads(l, h0).map(._1) = h0.map(._1) ⊦

Rule argument

Additional information

Used simplifier rules: a: ⊦ (x + y) + z = x + y + z; from specification list Used terms: v, false, l, l0, t, h0

Proof step 19 from proof event-persistDependentReads (previous step) (back to tree)

Lemma persistDependentReads-otherread

Proof step 20 from proof event-persistDependentReads (previous step) (back to tree)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

• Proof step 21:

  persistDependentReads(l0, h0).map(._1) ≠ h0.map(._1), ∀ l. persistDependentReads(l, h0).map(._1) = h0.map(._1) ⊦

Rule argument

Additional information

Used simplifier rules: persistDependentReads-read: ⊦ persistDependentReads(l, (R(t, l, v), b) ' + h) = (R(t, l, v), true) ' + persistDependentReads(l, h); a: ⊦ (x + y) + z = x + y + z; from specification list ⊦ # x = # z → (x + y = z + y0 ↔ x = z ∧ y = y0); (ws) ⊦ a + x = a ' + x; (s) ⊦ (a ' + x).map(f) = f(a) + x.map(f); (s)

Proof step 21 from proof event-persistDependentReads (previous step) (back to tree)

Heuristic quantifier closing applied rule all left

And closed the goal!

Rule argument

Additional information

Used terms: l0

Proof step 22 from proof event-persistDependentReads (previous step) (back to tree)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

• Proof step 23:

  persistDependentReads(l, h0).map(._1) ≠ h0.map(._1), l ≠ l0, ∀ l. persistDependentReads(l, h0).map(._1) = h0.map(._1) ⊦

Rule argument

Additional information

Used simplifier rules: a: ⊦ (x + y) + z = x + y + z; from specification list ⊦ # x = # z → (x + y = z + y0 ↔ x = z ∧ y = y0); (ws) ⊦ a + x = a ' + x; (s) ⊦ (a ' + x).map(f) = f(a) + x.map(f); (s)

Proof step 23 from proof event-persistDependentReads (previous step) (back to tree)

Heuristic quantifier closing applied rule all left

And closed the goal!

Rule argument

Additional information

Used terms: l

Proof step 24 from proof event-persistDependentReads (previous step) (back to tree)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

• Proof step 25:

  persistDependentReads(l, (W(t, l0, v), boolvar) ' + h0).map(._1) ≠ W(t, l0, v) ' + h0.map(._1), ∀ l. persistDependentReads(l, h0).map(._1) = h0.map(._1) ⊦

Rule argument

Additional information

Proof step 25 from proof event-persistDependentReads (previous step) (back to tree)

User applied rule apply rewrite lemma

And obtained the following new goals

• Proof step 26:

  ⊦ l ≠ l0 → persistDependentReads(l, (W(t, l0, v), b) ' + h) = (W(t, l0, v), b) ' + persistDependentReads(l, h)

• Proof step 27:

  ((W(t, l0, v), boolvar) ' + persistDependentReads(l, h0)).map(._1) ≠ W(t, l0, v) ' + h0.map(._1), l ≠ l0, ∀ l. persistDependentReads(l, h0).map(._1) = h0.map(._1) ⊦

Rule argument

Additional information

Used simplifier rules: persistDependentReads-nextwrite: ⊦ persistDependentReads(l, (W(t, l, v), b) ' + h) = (W(t, l, v), b) ' + h; ⊦ (a ' + x).map(f) = f(a) + x.map(f); (s) ⊦ a + x = a ' + x; (s) ⊦ # x = # z → (x + y = z + y0 ↔ x = z ∧ y = y0); (ws) a: ⊦ (x + y) + z = x + y + z; from specification list Used terms: v, boolvar, l, l0, t, h0

Proof step 26 from proof event-persistDependentReads (previous step) (back to tree)

Lemma persistDependentReads-otherwrite

Proof step 27 from proof event-persistDependentReads (previous step) (back to tree)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

• Proof step 28:

  persistDependentReads(l, h0).map(._1) ≠ h0.map(._1), l ≠ l0, ∀ l. persistDependentReads(l, h0).map(._1) = h0.map(._1) ⊦

Rule argument

Additional information

Used simplifier rules: a: ⊦ (x + y) + z = x + y + z; from specification list ⊦ # x = # z → (x + y = z + y0 ↔ x = z ∧ y = y0); (ws) ⊦ a + x = a ' + x; (s) ⊦ (a ' + x).map(f) = f(a) + x.map(f); (s)

Proof step 28 from proof event-persistDependentReads (previous step) (back to tree)

Heuristic quantifier closing applied rule all left

And closed the goal!

Rule argument

Additional information

Used terms: l