Nuprl Lemma : int-decr-map-isEmpty-assert

[Value:Type]. ∀[m:int-decr-map-type(Value)].
  uiff(↑int-decr-map-isEmpty(m);m int-decr-map-empty() ∈ int-decr-map-type(Value))


Proof




Definitions occuring in Statement :  int-decr-map-isEmpty: int-decr-map-isEmpty(m) int-decr-map-empty: int-decr-map-empty() int-decr-map-type: int-decr-map-type(Value) assert: b uiff: uiff(P;Q) uall: [x:A]. B[x] universe: Type equal: t ∈ T
Definitions unfolded in proof :  uall: [x:A]. B[x] member: t ∈ T uiff: uiff(P;Q) and: P ∧ Q uimplies: supposing a int-decr-map-isEmpty: int-decr-map-isEmpty(m) int-decr-map-type: int-decr-map-type(Value) int-decr-map-empty: int-decr-map-empty() so_lambda: λ2y.t[x; y] subtype_rel: A ⊆B so_lambda: λ2x.t[x] so_apply: x[s] all: x:A. B[x] top: Top so_apply: x[s1;s2] gt: i > j prop: assert: b ifthenelse: if then else fi  null: null(as) so_lambda: so_lambda(x,y,z,w.t[x; y; z; w]) so_apply: x[s1;s2;s3;s4] strict4: strict4(F) implies:  Q has-value: (a)↓ guard: {T} or: P ∨ Q squash: T nil: [] it: btrue: tt true: True pi1: fst(t) sq_stable: SqStable(P)

Latex:
\mforall{}[Value:Type].  \mforall{}[m:int-decr-map-type(Value)].
    uiff(\muparrow{}int-decr-map-isEmpty(m);m  =  int-decr-map-empty())



Date html generated: 2016_05_17-PM-01_48_41
Last ObjectModification: 2016_01_18-PM-06_42_25

Theory : datatype-signatures


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