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Proof step 7 from proof to-adrs-eq-app (previous step)

@(n, m, m2) ' + lax1.to-adr(n) = lax.to-adr(n) + @(n, m0, m1) ', lax = ladr + lax0, ∀ n, lax, m0, m1. lax1.to-adr(n) = lax.to-adr(n) + @(n, m0, m1) ' ∧ @(m0, m1) ∈ lax1 → lax1 = lax + @(m0, m1) ', @(n, m, m2) ∈ lax.to-adr(n) ∨ @(n, m, m2) = @(n, m0, m1), @(m0, m1) = @(m, m2) ∨ @(m0, m1) ∈ lax1, @(n, m0, m1) = @(n, m, m2) ∨ @(n, m0, m1) ∈ lax1.to-adr(n) ⊦ @(m, m2) ' + lax1 = lax + @(m0, m1) '

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
lax1.to-adr(n) = lax0.to-adr(n) + @(n, m0, m1) ', @(m0, m1) ∈ lax1, ∀ n, lax, m0, m1. lax1.to-adr(n) = lax.to-adr(n) + @(n, m0, m1) ' ∧ @(m0, m1) ∈ lax1 → lax1 = lax + @(m0, m1) ' ⊦ @(ladr.off, ladr.size) ' + lax1 = (ladr ' + lax0) + @(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);%to-adrs-in: ⊦ @(m, m0, m1) ∈ lax.to-adr(n) ↔ m = n ∧ @(m0, m1) ∈ lax;%in-15: ⊦ ax + adr ' = ax0 → adr ∈ ax0; (forward) from specification list[address-list-set]% ⊦ adr ∈ adr0 ' + ax ↔ adr = adr0 ∨ adr ∈ ax; (s)% ⊦ @(m, m0, m1) = @(m2, m3, m4) ↔ m = m2 ∧ m0 = m3 ∧ m1 = m4; (ws)% ⊦ adr ' + ax = adr0 ' + ax0 ↔ adr = adr0 ∧ ax = ax0; (ws)%a: ⊦ (ax + ax0) + ax1 = ax + ax0 + ax1; from specification list[address-list-set]%a: ⊦ (lax + lax0) + lax1 = lax + lax0 + lax1; from specification list[laddress-list]% ⊦ adr + ax = adr ' + ax; (s)% ⊦ ladr + lax = ladr ' + lax; (s)