Nuprl Lemma : inv_image_ind
∀[A:Type]. ∀[r:A ⟶ A ⟶ ℙ]. ∀[B:Type]. ∀f:B ⟶ A. (WellFnd{i}(A;x,y.r[x;y]) ⇒ WellFnd{i}(B;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
Lemmas referenced :
inv_image_ind_tp
Rules used in proof :
lemma_by_obid
Latex:
\mforall{}[A:Type]. \mforall{}[r:A {}\mrightarrow{} A {}\mrightarrow{} \mBbbP{}]. \mforall{}[B:Type].
\mforall{}f:B {}\mrightarrow{} A. (WellFnd\{i\}(A;x,y.r[x;y]) {}\mRightarrow{} WellFnd\{i\}(B;x,y.r[f x;f y]))
Date html generated:
2016_05_13-PM-03_18_25
Last ObjectModification:
2015_12_26-AM-09_06_48
Theory : well_fnd
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