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Proof step 15 from proof head-corr (conclusion)

inv(buf), abs(buf, a + x) ⊦ 〈head#(buf; b)〉 a = b

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 1:
⊦ abs(buf, x) ↔ buf .len = n→i(# x) ∧ x = tolist(buf, i→n(buf .len))
Proof step 14:
buf .len = 1 + n→i(# x), a ' + x = tolist(buf, i→n(buf .len)), inv(buf) ⊦ 〈head#(buf; b)〉 a = b

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ a ∈ b ' ↔ a = b], [CSIMPSEQ : ⊦ a ∈ x0 + x1 ↔ ¬ ¬ (a ∈ x0 ∨ a ∈ x1)], [CSIMPFORWARD : ⊦ a ' + x0 = x1 → a ∈ x1], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ n→i(m + n) = n→i(m) + n→i(n)], [CSIMPSEQ : ⊦ (x0 + x1) + x2 = x0 + x1 + x2], [CSIMPSEQ : ⊦ # a ' = 0 +1], [CSIMPSEQ : ⊦ # (x0 + x1) = # x0 + # x1], [CSIMPSEQ : ⊦ a + x0 = a ' + x0])]]