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Proof step 3 from proof to-adrs-eq-app (previous step)

(ladr + lax1).to-adr(n) = lax.to-adr(n) + @(n, m0, m1) ', @(m0, m1) ∈ ladr + lax1, ∀ n, lax, m0, m1. lax1.to-adr(n) = lax.to-adr(n) + @(n, m0, m1) ' ∧ @(m0, m1) ∈ lax1 → lax1 = lax + @(m0, m1) ' ⊦ ladr + lax1 = lax + @(m0, m1) '

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
@(n, ladr.off, ladr.size) ' + lax1.to-adr(n) = lax.to-adr(n) + @(n, m0, m1) ', ∀ n, lax, m0, m1. lax1.to-adr(n) = lax.to-adr(n) + @(n, m0, m1) ' ∧ @(m0, m1) ∈ lax1 → lax1 = lax + @(m0, m1) ', @(m0, m1) = ladr ∨ @(m0, m1) ∈ lax1, @(n, ladr.off, ladr.size) ∈ lax.to-adr(n) ∨ @(n, ladr.off, ladr.size) = @(n, m0, m1), @(n, m0, m1) = @(n, ladr.off, ladr.size) ∨ @(n, m0, m1) ∈ lax1.to-adr(n) ⊦ ladr ' + lax1 = lax + @(m0, m1) '

Rule argument

Additional information

Used simplifier rules: adrs-rec: ⊦ (ladr ' + lax).to-adr(n) = @(n, ladr.off, ladr.size) + lax.to-adr(n);% ⊦ adr ∈ adr0 ' + ax ↔ adr = adr0 ∨ adr ∈ ax; (s)% ⊦ adr ∈ adr0 ' ↔ adr = adr0; (s)% ⊦ adr ∈ ax + ax0 ↔ adr ∈ ax ∨ adr ∈ ax0; (s)%in-15: ⊦ ax + adr ' = ax0 → adr ∈ ax0; (forward) from specification list[address-list-set]%a: ⊦ (ax + ax0) + ax1 = ax + ax0 + ax1; from specification list[address-list-set]%in-14: ⊦ adr ' + ax = ax0 → adr ∈ ax0; (forward) from specification list[address-list-set]% ⊦ ladr ∈ ladr0 ' + lax ↔ ladr = ladr0 ∨ ladr ∈ lax; (s)%a: ⊦ (lax + lax0) + lax1 = lax + lax0 + lax1; from specification list[laddress-list]% ⊦ adr + ax = adr ' + ax; (s)% ⊦ ladr + lax = ladr ' + lax; (s)