Nuprl Lemma : inv_image_ind_a
∀[T:Type]. ∀[r:T ⟶ T ⟶ ℙ]. ∀[S:Type]. ∀f:S ⟶ T. (WellFnd{i}(T;x,y.r[x;y]) ⇒ WellFnd{i}(S;x,y.r[f x;f y]))
Proof
Definitions occuring in Statement :
wellfounded: WellFnd{i}(A;x,y.R[x; y]),
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s1;s2],
all: ∀x:A. B[x],
implies: P ⇒ Q,
apply: f a,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
wellfounded: WellFnd{i}(A;x,y.R[x; y]),
guard: {T},
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
wellfounded_wf,
all_wf,
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
sqequalRule,
lambdaEquality,
applyEquality,
hypothesis,
functionEquality,
Error :inhabitedIsType,
Error :functionIsType,
Error :universeIsType,
universeEquality,
independent_functionElimination,
because_Cache,
dependent_functionElimination,
equalitySymmetry,
hyp_replacement,
applyLambdaEquality
Latex:
\mforall{}[T:Type]. \mforall{}[r:T {}\mrightarrow{} T {}\mrightarrow{} \mBbbP{}]. \mforall{}[S:Type].
\mforall{}f:S {}\mrightarrow{} T. (WellFnd\{i\}(T;x,y.r[x;y]) {}\mRightarrow{} WellFnd\{i\}(S;x,y.r[f x;f y]))
Date html generated:
2019_06_20-AM-11_19_12
Last ObjectModification:
2018_09_26-AM-10_41_44
Theory : well_fnd
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