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Proof step 15 from proof inv-transaction (previous step)

jvalid1 ↔ true, jvalid ↔ # ndx0 = 1, gnd = mkgnode(ndx0.head, jmaxino0 + # gndx, jvalid0, jvalid), gndx0 = [], jmaxino0 = jmaxino1, jmaxino2 = 0, ndx2 = ndx, ∃ ndx. ( ndx2 = ndx + ndx0 ∧ (ndx0 = [] → transaction(ndx2, gndx)) ∧ (ndx0 ≠ [] → transaction-prefix(ndx2, gndx) ∧ # gndx = # ndx) ∧ jmaxino = gndx.flashsize ∧ (jvalid0 ↔ ndx = [])) ∧ ndx0 = ndx1 ⊦ ndx0 = [], ∃ ndx. ( ndx2 = ndx + ndx0.tail ∧ (ndx0.tail = [] → transaction(ndx2, gndx + gnd)) ∧ (ndx0.tail ≠ [] → transaction-prefix(ndx2, gndx + gnd) ∧ #(gndx + gnd) = # ndx) ∧ jmaxino + gnd.flashsize = (gndx + gnd).flashsize ∧ (false ↔ ndx = [])) ∧ # ndx0.tail < # ndx1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 16:
# gndx = # ndx3, transaction-prefix(ndx3 + ndx1, gndx) ⊦ ndx1 = [], ∃ ndx. ndx3 + ndx1 = ndx + ndx1.tail ∧ (ndx1.tail = [] → transaction(ndx3 + ndx1, gndx + mkgnode(ndx1.head, jmaxino0 + # ndx3, ndx3 = [], # ndx1 = 1) ')) ∧ ( ndx1.tail ≠ [] → transaction-prefix(ndx3 + ndx1, gndx + mkgnode(ndx1.head, jmaxino0 + # ndx3, ndx3 = [], # ndx1 = 1) ') ∧ # ndx3 + 1 = # ndx) ∧ ndx ≠ []

Rule argument

Additional information

Used simplifier rules: ⊦ ¬ n < n; (s)% ⊦ m < n + 1 ↔ ¬ n < m; (s)%n0 ≤ n ⊦ n - n0 < m ↔ n < m + n0; (s)% ⊦ # ndx = 0 ↔ ndx = []; (s)% ⊦ m < 1 ↔ m = 0; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ n -1 = n - 1; (s)% ⊦ ndx ≠ [] → # ndx.tail = (# ndx)-1; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + n = m + n0 ↔ n = n0; (s)% ⊦ gnd '.flashsize = gnd.flashsize; (s)% ⊦ (gndx + gndx0).flashsize = gndx.flashsize + gndx0.flashsize; (s)%a: ⊦ (gndx + gndx0) + gndx1 = gndx + gndx0 + gndx1; from specification list[group-store]% ⊦ # gnd ' = 0 +1; (s)% ⊦ #(gndx + gndx0) = # gndx + # gndx0; (s)% ⊦ gndx + gnd = gndx + gnd '; (s)