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Proof step 2 from proof Data-in-putdelput (previous step)

a0 ∈ (st[b, d1] -- a)[c, d2] ⊦ (st[b, d1] -- a)[c, d2][a0] = d1, (st[b, d1] -- a)[c, d2][a0] = d2, ∃ a1. a1 ∈ st ∧ st[a1] = (st[b, d1] -- a)[c, d2][a0]

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Proof step 3:
a0 ∈ (st[b, d1] -- a)[c, d2] ⊦ a0 = c, (st[b, d1] -- a)[c, d2][a0] = d1, (st[b, d1] -- a)[c, d2][a0] = d2, ∃ a1. a1 ∈ st ∧ st[a1] = (st[b, d1] -- a)[c, d2][a0]

Rule argument

fma: a0 = c

Additional information

Used simplifier rules: At-same: ⊦ st[a, d][a] = d; from specification store Used formulas: a0 = c