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Proof step 14 from proof to-adrs-sublist (previous step)

m1 ≤ # lax0, # @(m, m0) ' ≤ m1 + 1, ∀ n0, n1, n. n0 + n1 ≤ # lax0 → sublist(n0, n1, lax0.to-adr(n)) = sublist(n0, n1, lax0).to-adr(n) ⊦ @(n, m, m0) ' + sublist(0, m1, lax0.to-adr(n)) = (@(m, m0) ' + sublist(0, m1 + 1 - # @(m, m0) ', lax0)).to-adr(n)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 15:
m1 ≤ # lax0, ∀ n0, n1, n. n0 + n1 ≤ # lax0 → sublist(n0, n1, lax0.to-adr(n)) = sublist(n0, n1, lax0).to-adr(n) ⊦ sublist(0, m1, lax0.to-adr(n)) = sublist(0, m1, lax0).to-adr(n)

Rule argument

Additional information

Used simplifier rules: adrs-rec: ⊦ (ladr ' + lax).to-adr(n) = @(n, ladr.off, ladr.size) + lax.to-adr(n);% ⊦ m ≤ m + n; (s)%a: ⊦ (ax + ax0) + ax1 = ax + ax0 + ax1; from specification list[address-list-set]% ⊦ adr ' + ax = adr ' + ax0 ↔ ax = ax0; (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)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ n + 0 = n; (s)% ⊦ n ≤ m → m + n0 - n = (m - n) + n0; (s)% ⊦ # ladr ' = 0 +1; (s)