Used simplifier rules/spec theorems by specification

Used from specification nat-basic

• nat-basic/a is used by subarray-split-size, subarray-split-first, subarray-split-at, subarray-eq-elim, subarray-emparray, subarray-elim-right, subarray-elim, subarray-append-shift-right-simp-0, subarray-append-shift-right, subarray-append-shift-left, subarray-append-left-01, subarray-append-left, subarray-append-elim-left0-simp, subarray-append-elim-left, subarray-append-elim, subarray-append-consec0, subarray-append-consec, splice-resize-less, splice-len, same-size-append, rangeeq-write-left-below, rangeeq-write-left-above, range-extend, range-eq-splice-less, range-eq-shift-right, range-eq-resize, range-eq-ext, range-eq-cut, range-eq-bounds, range-eq-append-shift, range-eq-append, range-copy-upper, range-copy-outer, range-copy-lower, range-copy-inner, range-copy-drop, mkemparray-append, fill2append, fill-append-shift, copy2append00, copy2append0, copy2append, copy-shift-right, copy-shift-append, copy-exact-append, copy-append, array-split2, array-split1, array-split-elim-size, append-zero-right, append-zero-left, append-prefix-left, append-len, append-left-size0, append-inj, append-eq-right, append-eq-left, append-eq-emptyar, append-atp2, append-at2, append-at1-simp2, append-at1-simp1, append-at1, append-at, append-a,
• nat-basic/add-base is used by subarray-split-size, subarray-split-first, subarray-split-at, subarray-eq-elim, subarray-append-shift-right, subarray-append-left-01, subarray-append-left, subarray-append-elim-left0-simp, subarray-append-consec0, splice-resize-less, range-eq-splice-less, range-eq-ext, range-eq-bounds, range-eq-append, fill2append, copy2append00, copy2append0, copy2append, copy-shift-append, copy-exact-append, append-zero-right, append-zero-left, append-prefix-left, append-left-size0, append-atp2,
• nat-basic/c is used by subarray-split-size, subarray-split-first, subarray-split-at, subarray-eq-elim, subarray-emparray, subarray-elim-right, subarray-elim, subarray-append-shift-right-simp-0, subarray-append-shift-right, subarray-append-shift-left, subarray-append-left-01, subarray-append-left, subarray-append-elim-left0-simp, subarray-append-elim-left, subarray-append-elim, subarray-append-consec0, subarray-append-consec, splice-resize-less, splice-len, same-size-append, rangeeq-write-left-below, rangeeq-write-left-above, range-extend, range-eq-splice-less, range-eq-shift-right, range-eq-resize, range-eq-ext, range-eq-cut, range-eq-bounds, range-eq-append-shift, range-eq-append, range-copy-upper, range-copy-outer, range-copy-lower, range-copy-inner, range-copy-drop, mkemparray-append, fill2append, fill-append-shift, copy2append00, copy2append0, copy2append, copy-shift-right, copy-shift-append, copy-exact-append, copy-append, array-split2, array-split1, array-split-elim-size, append-zero-right, append-zero-left, append-prefix-left, append-len, append-left-size0, append-inj, append-eq-right, append-eq-left, append-eq-emptyar, append-atp2, append-at2, append-at1-simp2, append-at1-simp1, append-at1, append-at, append-a,
• nat-basic/eq-01 is used by subarray-split-size, subarray-split-first, subarray-eq-elim, subarray-append-shift-right, subarray-append-shift-left, subarray-append-consec, splice-resize-less, splice-len, range-copy-inner, mkemparray-append, fill-append-shift, copy-shift-right, array-split-elim-size, append-len, append-inj, append-eq-right, append-eq-left, append-a,
• nat-basic/eq-02 is used by subarray-eq-elim, same-size-append, copy2append00, array-split1, array-split-elim-size, append-prefix-left, append-left-size0,
• nat-basic/f is used by subarray-split-size, subarray-split-first, subarray-split-at, subarray-eq-elim, subarray-emparray, subarray-elim-right, subarray-elim, subarray-append-shift-right, subarray-append-shift-left, subarray-append-elim-left0-simp, subarray-append-consec, splice-resize-less, resize-twice, rangeeq-write-left-below, range-extend, range-eq-trans, range-eq-subarrays, range-eq-splice-less, range-eq-shift-right, range-eq-resize, range-eq-refl-simp, range-eq-extract, range-eq-ext, range-eq-bounds, range-eq-append, range-copy-upper, range-copy-outer, range-copy-lower, range-copy-inner, range-copy-drop, mkemparray-append, fill2append, fill-append-shift, copy2append00, copy2append0, copy2append, copy-shift-right, copy-exact-append, copy-append, array-split2, array-split1, array-split-elim-size, append-zero-left, append-prefix-left, append-left-size0, append-inj, append-eq-right, append-eq-left, append-atp2, append-at2, append-at1-simp2, append-at1-simp1, append-at1, append-at, append-a,
• nat-basic/l is used by subarray-split-size, subarray-split-at, subarray-eq-elim, subarray-emparray, subarray-elim, subarray-append-shift-right, subarray-append-shift-left, subarray-append-consec, splice-resize-less, range-extend, range-eq-splice-less, range-copy-upper, range-copy-outer, range-copy-lower, range-copy-inner, mkemparray-append, fill2append, fill-append-shift, copy2append0, copy2append, copy-shift-right, array-split2, array-split1, array-split-elim-size, append-inj, append-eq-left, append-atp2, append-at2, append-at1-simp1, append-a,
• nat-basic/l-01 is used by subarray-split-size, subarray-split-at, subarray-eq-elim, subarray-append-shift-right, subarray-append-consec, splice-resize-less, range-extend, range-copy-upper, range-copy-lower, range-copy-inner, range-copy-drop, mkemparray-append, fill2append, fill-append-shift, copy2append0, copy2append, copy-shift-right, copy-append, append-at2, append-a,
• nat-basic/l-02 is used by subarray-eq-elim, splice-resize-less, rangeeq-write-left-below, range-extend, range-eq-splice-less, range-eq-append, range-copy-upper, range-copy-outer, range-copy-lower, range-copy-inner, range-copy-drop, fill-append-shift, copy2append00, copy2append0, copy2append, copy-shift-right, append-inj, append-eq-right, append-atp2, append-at1, append-a,
• nat-basic/l-04 is used by range-eq-splice-less,
• nat-basic/l-06 is used by fill2append, copy2append0, copy2append, append-at1-simp2,
• nat-basic/l-08 is used by append-a,
• nat-basic/lf is used by subarray-elim, splice-resize-less, copy2append00, copy2append0, array-split2,
• nat-basic/lf-01 is used by subarray-split-at, subarray-eq-elim, subarray-elim, fill2append, copy2append0, copy2append, copy-exact-append, array-split2, array-split1, array-split-elim-size, append-inj, append-eq-right, append-eq-left,
• nat-basic/lf-02 is used by subarray-eq-elim, subarray-elim, copy2append00, array-split2, array-split1, array-split-elim-size,
• nat-basic/ls-02 is used by subarray-eq-elim, subarray-elim, subarray-append-shift-right, array-split2, array-split1, array-split-elim-size, append-at1-simp1,
• nat-basic/neq-01 is used by copy2append0, copy2append,
• nat-basic/one-01 is used by subarray-split-first,
• nat-basic/oz is used by subarray-split-first,
• nat-basic/ref is used by subarray-eq-elim, subarray-elim, subarray-append-left, fill2append, copy2append, array-split2, array-split1, array-split-elim-size, append-inj, append-eq-right,
• nat-basic/s-04 is used by subarray-split-first, range-eq-ext,
• nat-basic/succ is used by splice-resize-less, range-eq-ext, range-eq-bounds, range-eq-append, copy2append00, copy2append0,
• nat-basic/trans is used by splice-resize-less, copy2append00, copy2append0,
• nat-basic/z-01 is used by subarray-eq-elim, append-eq-emptyar,
• nat-basic/zero-01 is used by subarray-split-size, range-eq-ext, copy-exact-append,

Used from specification min-max

• min-max/max is used by splice-resize-less, range-eq-splice-less,
• min-max/min is used by splice-resize-less,
• min-max/max-first-ls is used by splice-resize-less, splice-len, range-eq-splice-less,
• min-max/max-notls1 is used by splice-resize-less,
• min-max/max-notls2 is used by splice-resize-less,
• min-max/max-second-le is used by splice-resize-less, splice-len, range-eq-splice-less,

Used from specification nat

• nat/le-addex is used by range-eq-splice-less, range-copy-lower, range-copy-inner,
• nat/add-01 is used by splice-resize-less, range-extend, range-copy-upper, range-copy-lower, range-copy-inner, range-copy-drop, copy2append, copy-shift-right, copy-append,
• nat/cancel-01 is used by subarray-eq-elim, subarray-append-shift-left, range-extend, range-eq-splice-less, range-copy-upper, range-copy-lower, range-copy-inner,
• nat/elim-pred-c is used by subarray-split-first,
• nat/elim-sub is used by subarray-split-size, subarray-split-at, subarray-eq-elim, subarray-elim, subarray-append-shift-right, subarray-append-shift-left, subarray-append-elim-left, subarray-append-consec, splice-resize-less, range-extend, range-eq-append-shift, range-copy-upper, range-copy-outer, range-copy-lower, range-copy-inner, mkemparray-append, fill2append, fill-append-shift, copy2append00, copy2append0, copy2append, copy-shift-right, copy-append, array-split2, array-split1, append-at2, append-a,
• nat/eq-01 is used by subarray-eq-elim, subarray-append-shift-right-simp-0, subarray-append-elim-left, splice-resize-less, range-extend, range-copy-upper, range-copy-outer, range-copy-lower, range-copy-inner, copy2append00, copy2append0, copy-shift-right, append-atp2,
• nat/fle is used by subarray-emparray, subarray-append-elim-left0-simp, splice-resize-less, resize-twice, range-eq-splice-less, range-eq-resize, range-copy-upper, range-copy-drop, fill2append, copy2append00, copy2append0, copy2append, append-inj, append-eq-right, append-at1-simp1,
• nat/fle-01 is used by subarray-split-size, subarray-split-at, subarray-eq-elim, subarray-elim, subarray-append-shift-right, subarray-append-elim-left0-simp, subarray-append-consec, splice-resize-less, resize-twice, range-extend, range-eq-splice-less, range-eq-append, range-copy-upper, range-copy-outer, range-copy-lower, range-copy-inner, range-copy-drop, mkemparray-append, fill2append, fill-append-shift, copy2append0, copy2append, copy-shift-right, copy-append, array-split2, append-left-size0, append-inj, append-eq-right, append-at2, append-at1, append-a,
• nat/ge is used by range-eq-append-shift,
• nat/le-add is used by subarray-eq-elim,
• nat/le-def is used by subarray-split-first, subarray-eq-elim, subarray-elim, subarray-append-left-01, subarray-append-left, splice-resize-less, splice-len, resize-twice, range-eq-bounds, range-eq-append, range-copy-upper, range-copy-outer, range-copy-lower, range-copy-inner, range-copy-drop, copy2append00, copy2append0, copy2append, copy-shift-right, copy-append, array-split2, array-split1, array-split-elim-size,
• nat/le-ls-simp is used by subarray-split-size, subarray-split-first, subarray-append-shift-right, subarray-append-left-01, splice-resize-less, resize-twice, range-eq-splice-less, range-eq-bounds, range-copy-upper, range-copy-outer, range-copy-inner, fill2append, fill-append-shift, copy2append0, copy2append, append-at2, append-a,
• nat/le-sum is used by range-eq-splice-less,
• nat/lels is used by subarray-split-size, subarray-split-first, subarray-split-at, subarray-emparray, subarray-elim-right, subarray-append-shift-right, subarray-append-shift-left, subarray-append-elim-left0-simp, subarray-append-elim, subarray-append-consec, splice-resize-less, range-extend, range-eq-splice-less, range-eq-shift-right, range-eq-resize, range-eq-ext, range-eq-bounds, range-copy-upper, range-copy-outer, range-copy-lower, range-copy-inner, range-copy-drop, mkemparray-append, fill2append, fill-append-shift, copy2append0, copy2append, copy-shift-right, copy-append, append-inj, append-eq-right, append-eq-left, append-atp2, append-at2, append-at1-simp1, append-at1, append-at, append-a,
• nat/lels-02 is used by subarray-elim, subarray-append-shift-right, copy2append00, copy2append0, copy2append, array-split2,
• nat/lels-03 is used by subarray-split-at, splice-resize-less, copy2append0, copy2append, array-split2,
• nat/lels-04 is used by range-copy-inner,
• nat/lep is used by subarray-split-size, subarray-split-first, subarray-split-at, subarray-eq-elim, subarray-elim, subarray-append-shift-right-simp-0, subarray-append-shift-right, subarray-append-shift-left, subarray-append-elim-left, subarray-append-consec, splice-resize-less, range-extend, range-copy-upper, range-copy-outer, range-copy-lower, range-copy-inner, mkemparray-append, fill2append, fill-append-shift, copy2append00, copy2append0, copy2append, copy-shift-right, copy-append, array-split1, append-at2, append-a,
• nat/lep-02 is used by subarray-eq-elim, subarray-elim-right, subarray-elim, subarray-append-shift-right-simp-0, subarray-append-shift-right, subarray-append-shift-left, subarray-append-elim-left, splice-resize-less, rangeeq-write-left-above, range-extend, range-eq-splice-less, range-eq-shift-right, range-eq-resize, range-eq-cut, range-copy-upper, range-copy-outer, range-copy-lower, range-copy-inner, range-copy-drop, fill-append-shift, copy2append0, copy2append, copy-shift-right, copy-shift-append, copy-append, append-atp2, append-a,
• nat/ler is used by subarray-eq-elim, subarray-elim, range-eq-cut, copy-shift-append,
• nat/let is used by subarray-split-first, subarray-elim-right, subarray-append-shift-right, subarray-append-elim-left0-simp, resize-twice, range-extend, range-eq-shift-right, range-eq-resize, range-copy-upper, range-copy-outer, range-copy-lower, range-copy-inner, range-copy-drop, fill2append, copy2append, copy-append,
• nat/lez is used by splice-resize-less, append-left-size0,
• nat/lez-01 is used by subarray-eq-elim, range-eq-splice-less,
• nat/ls-02 is used by range-copy-inner, copy2append0, copy2append, copy-append,
• nat/ls-le-simp is used by subarray-split-size, subarray-emparray, subarray-elim-right, subarray-append-shift-left, subarray-append-elim-left0-simp, subarray-append-elim, splice-resize-less, resize-exact, rangeeq-write-left-above, range-extend, range-eq-splice-less, range-eq-shift-right, range-eq-resize, range-copy-upper, range-copy-outer, range-copy-lower, range-copy-inner, range-copy-drop, mkemparray-append, fill2append, fill-append-shift, copy2append0, copy2append, copy-shift-right, copy-exact-append, copy-append, append-inj, append-eq-left, append-atp2, append-at1,
• nat/not-zero is used by subarray-split-first,
• nat/sub-base is used by subarray-split-size, subarray-eq-elim, copy2append00, copy-exact-append, append-left-size0,
• nat/succ-01 is used by subarray-split-first, range-eq-ext, range-eq-bounds,
• nat/zero is used by subarray-eq-elim, copy-shift-append,
• nat/zero-01 is used by subarray-split-at,

Used from specification array-copy

• array-copy/Subarray is used by subarray-split-size, subarray-append-elim-left0, subarray-append-elim-left,
• array-copy/at-copy is used by subarray-split-size, splice-resize-less, range-extend, range-eq-splice-less, range-copy-upper, range-copy-outer, range-copy-lower, range-copy-inner, range-copy-drop, copy-shift-right, append-atp2, append-at1,
• array-copy/at-fill is used by subarray-emparray,
• array-copy/at-fill-h is used by fill2append, fill-append-shift,
• array-copy/subarray-at is used by subarray-split-first,
• array-copy/subarray-subarray-elim is used by subarray-eq-elim,
• array-copy/at-copy is used by splice-resize-less, copy2append0, copy2append, copy-shift-right, copy-shift-append, copy-exact-append, copy-append,
• array-copy/at-fill-mkarray is used by zarray-at, subarray-emparray, mkemparray-append, fill2append, emparray-at,
• array-copy/copy-exact is used by copy2append00, append-zero-left,
• array-copy/size-copy is used by subarray-split-size, splice-len, range-extend, range-eq-splice-less, range-copy-upper, range-copy-outer, range-copy-lower, range-copy-inner, range-copy-drop, copy2append0, copy2append, copy-shift-right, copy-shift-append, copy-exact-append, copy-append, append-len,
• array-copy/size-fill is used by zarray-len, subarray-emparray, mkemparray0-append-right, mkemparray0-append-left, mkemparray-eq, mkemparray-append, fill2append, emparray-len,
• array-copy/size-fill-h is used by fill2append, fill-append-shift,
• array-copy/size-subarray is used by subarray-split-first, subarray-split-at, subarray-same-ar-eq, subarray-eq-elim, subarray-emparray, subarray-elim-right, subarray-elim, subarray-append-shift-right, subarray-append-shift-left, subarray-append-elim-left0-simp, subarray-append-elim, subarray-append-consec, range-eq-subarrays, fill2append, copy2append00, copy2append0, copy2append, array-split2, array-split1, array-split-elim-size,
• array-copy/subarray-at is used by subarray-split-first, subarray-split-at, subarray-emparray, subarray-elim-right, subarray-append-shift-right, subarray-append-shift-left, subarray-append-elim-left0-simp, subarray-append-elim, subarray-append-consec, range-eq-subarrays, fill2append, copy2append0, copy2append,
• array-copy/subarray-elim is used by subarray-split-at, subarray-eq-elim, subarray-elim, subarray-append-shift-right, subarray-append-left, fill2append, copy2append00, copy2append0, copy2append, array-split2, array-split1, array-split-elim-size,
• array-copy/subarray-zero is used by subarray-eq-elim, copy2append00,

Used from specification array

• array/Extension is used by subarray-split-size, subarray-split-first, subarray-split-at, subarray-same-ar-eq, subarray-emparray, subarray-elim-right, subarray-append-shift-right, subarray-append-shift-left, subarray-append-elim-left0-simp, subarray-append-elim, subarray-append-consec, splice-resize-less, resize-twice, resize-exact, range-eq-subarrays, mkemparray-eq, mkemparray-append, fill2append, fill-append-shift, copy2append0, copy2append, copy-shift-right, copy-shift-append, copy-exact-append, copy-append, append-zero-right, append-zero-left, append-prefix-left, append-left-size0, append-inj, append-eq-right, append-eq-left, append-eq-emptyar, append-a,
• array/Size-mkarray is used by zarray-len, subarray-split-size, subarray-split-first, subarray-eq-elim, subarray-emparray, mkemparray0-append-right, mkemparray0-append-left, mkemparray-eq, mkemparray-append, fill2append, emparray-len, append-zero-right, append-zero-left, append-eq-emptyar,
• array/Size-put is used by subarray-split-first, rangeeq-write-left-below, rangeeq-write-left-above,
• array/cgetput is used by subarray-split-first,
• array/cngetput is used by rangeeq-write-left-below, rangeeq-write-left-above,
• array/size-0 is used by subarray-eq-elim, same-size-append, append-eq-emptyar,