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Proof step 15 from proof ladrlist-to-adr-split (previous step)

lax0.to-adr(m)[m5] = @(m0, m1, m2), m5 < # lax0, m5 < # lax0 → (lax0.to-adr(m)[m5] = @(m0, m1, m2) ↔ (∃ lax2, lax1. lax0 = lax2 + @(m1, m2) ' + lax1 ∧ m0 = m ∧ # lax2 = m5)), ∀ n, m6, m7, m8, m9. n < # lax0 → (lax0.to-adr(m6)[n] = @(m7, m8, m9) ↔ (∃ lax2, lax1. lax0 = lax2 + @(m8, m9) ' + lax1 ∧ m7 = m6 ∧ # lax2 = n)) ⊦ lax0 = [], ∃ lax, lax1. @(m3, m4) ' + lax0 = lax + @(m1, m2) ' + lax1 ∧ m0 = m ∧ # lax = m5 + 1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 16:
(lax.to-adr(m) + @(m, m1, m2) ' + lax1.to-adr(m))[# lax] = @(m, m1, m2), ∀ n, m0, m5, m6, m7. ¬ # lax + # lax1 < n → ( (lax.to-adr(m0) + @(m0, m1, m2) ' + lax1.to-adr(m0))[n] = @(m5, m6, m7) ↔ (∃ lax2, lax3. lax + @(m1, m2) ' + lax1 = lax2 + @(m6, m7) ' + lax3 ∧ m5 = m0 ∧ # lax2 = n)) ⊦ ∃ lax2, lax3. @(m3, m4) ' + lax + @(m1, m2) ' + lax1 = lax2 + @(m1, m2) ' + lax3 ∧ # lax2 = # lax + 1

Rule argument

Additional information

Used simplifier rules: c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ ¬ m + n < m; (s)% ⊦ m < n + 1 ↔ ¬ n < m; (s)% ⊦ m +1 = m + 1; (s)% ⊦ #(ladr ' + lax) = (# lax)+1; (s)% ⊦ #(lax + lax0) = # lax + # lax0; (s)% ⊦ lax + ladr ' + lax0 ≠ []; (s)%a: ⊦ (lax + lax0) + lax1 = lax + lax0 + lax1; from specification list[laddress-list]% ⊦ adr + ax = adr ' + ax; (s)% ⊦ @(m, m0).size = m0; (s)% ⊦ @(m, m0).off = m; (s)%⊦ (ladr ' + lax).to-adr(n) = @(n, ladr.off, ladr.size) + lax.to-adr(n); (s)% ⊦ (lax0 + lax1).to-adr(n) = lax0.to-adr(n) + lax1.to-adr(n); (s)%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic