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Proof step 46 from proof datasize-append-empty-h (previous step)

m ≤ # buf0 + # buf1, # buf0 ≤ m → datasize(buf1, m - # buf0) = 0 ⊦ datasize(buf0 + buf1, m) = datasize(buf0, min(m, # buf0))

User applied rule structural induction

And obtained the following new goals

Proof step 1:
m ≤ # buf0 ⊦ datasize(buf0 + buf1, m) = datasize(buf0, m)

Rule argument

indvar: m

Additional information

[Concretesimprules((Csimpnamedseq(datasize-append-lower-h,,, m ≤ # buf0 ⊦ datasize(buf0 + buf1, m) = datasize(buf0, m)) Csimpnamedseq(datasize-base,,, ⊦ datasize(buf, 0) = 0) Csimpgen(nat freely generated by 0, +1;) Csimpnamedseq(nat,,lez, ⊦ 0 ≤ m) Csimpnamedseq(array-splice,buffer,append-a, ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1) Csimpnamedseq(min-max,,min-0-left, ⊦ min(0, n) = 0)))]