Thm* A:Type, eq:EqDecider(A), f:a:A fp-> Top.
Thm* fpf-dom-list(f) {a:A| a dom(f) } List | [fpf-dom-list_wf] |
Thm* eq:EqDecider(A), B:Top, f:a:A fp-> Top. || f | [fpf-empty-compatible-left] |
Thm* eq:EqDecider(A), B:Top, f:a:A fp-> Top. f || | [fpf-empty-compatible-right] |
Thm* eq:EqDecider(A), P:(A Type Prop), x:A, v:Type.
Thm* y dom(x : v). w=x : v(y)  P(y,w)  P(x,v) | [fpf-all-single-decl] |
Thm* eq:EqDecider(A), x,y:A, v:Top. x dom(y : v) ~ (eqof(eq)(y,x)) | [fpf-single-dom-sq] |
Thm* eq:EqDecider(A), x,y:A, v:Top. x dom(y : v)  x = y | [fpf-single-dom] |
Thm* eq:EqDecider(A), x:A, v,P:Top. z != x : v(x) ==> P(a,z) ~ (True  P(x,v)) | [fpf-val-single1] |
Thm* eq:EqDecider(A), x,y:A, v,z:Top.
Thm* x : v(y)?z ~ if eqof(eq)(x,y) v else z fi | [fpf-cap-single] |
Thm* eq:EqDecider(A), x:A, v,z:Top. x : v(x)?z ~ v | [fpf-cap-single1] |
Thm* eq:EqDecider(A), f:a:A fp-> Top, g:Top, x:A.
Thm* f g(x) ~ if x dom(f) f(x) else g(x) fi | [fpf-join-ap-sq] |
Thm* eq:EqDecider(A), f,g:x:A fp-> Top.
Thm* fpf-is-empty(f g) ~ (fpf-is-empty(f) fpf-is-empty(g)) | [fpf-join-is-empty] |
Thm* eq:EqDecider(A), f,g:a:A fp-> Top, x:A.
Thm* x dom(f g)  x dom(f) x dom(g) | [fpf-join-dom2] |
Thm* B:(A Type), eq:EqDecider(A), f,g:a:A fp-> B(a), x:A.
Thm* x dom(f g)  x dom(f) x dom(g) | [fpf-join-dom] |